hdu 5514(容斥原理)

<div class="vj_description" style="color: rgb(34, 34, 34); font-family: Verdana, Arial, sans-serif; font-size: 14px;"><p class="pst" style="margin-bottom: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 18pt; font-weight: bold; color: blue;">Description</p><div class="textBG" style="border-radius: 10px; padding: 10px; border: 2px dotted; font-family: "Times New Roman", Times, serif; font-size: 17px; background-color: rgb(234, 235, 255);"><div class="panel_content">There are <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-1-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.974em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.917em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.511em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-2" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mi" id="MathJax-Span-3" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006D.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 16px; height: 9px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.591em;"></span></span></nobr></span> stones lying on a circle, and <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-2-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-4" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.688em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.631em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.511em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-5" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mi" id="MathJax-Span-6" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006E.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 11px; height: 9px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.591em;"></span></span></nobr></span> frogs are jumping over them. The stones are numbered from <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-3-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-7" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.631em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.574em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.374em 1000em 2.401em -0.454em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-8" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mn" id="MathJax-Span-9" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0030.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 13px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.885em;"></span></span></nobr></span> to <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-4-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-10" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 2.858em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 2.744em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.374em 1000em 2.401em -0.511em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-11" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mi" id="MathJax-Span-12" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006D.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 16px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span class="mo" id="MathJax-Span-13" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.231em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/2212.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.117em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 4px; width: 13px; height: 1px; display: inline !important; float: none !important;" alt="" /></span><span class="mn" id="MathJax-Span-14" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.231em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0031.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 8px; height: 12px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.885em;"></span></span></nobr></span> and the frogs are numbered from <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-5-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-15" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.574em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.517em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.374em 1000em 2.401em -0.397em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-16" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mn" id="MathJax-Span-17" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0031.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 8px; height: 12px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.826em;"></span></span></nobr></span> to <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-6-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-18" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.688em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.631em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.511em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-19" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mi" id="MathJax-Span-20" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006E.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 11px; height: 9px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.591em;"></span></span></nobr></span>. The <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-7-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-21" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.403em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.403em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.374em 1000em 2.401em -0.511em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-22" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mi" id="MathJax-Span-23" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0069.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 6px; height: 13px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.885em;"></span></span></nobr></span>-th frog can jump over exactly <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-8-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-24" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.917em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.86em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.573em -0.454em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-25" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-26" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.86em; height: 0px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.454em); top: -2.224em; left: 0.003em;"><span class="mi" id="MathJax-Span-27" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0061.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; top: -2.053em; left: 0.517em;"><span class="mi" id="MathJax-Span-28" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; font-size: 12.3796px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/283/0069.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 4px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.232em; overflow: hidden; width: 0px; height: 0.768em;"></span></span></nobr></span> stones in a single step, which means from stone <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-9-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-29" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 4.115em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 4.001em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.316em 1000em 2.63em -0.511em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-30" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mi" id="MathJax-Span-31" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006A.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -4px; width: 8px; height: 16px; display: inline !important; float: none !important;" alt="" /></span><span class="mtext" id="MathJax-Span-32" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/00A0.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.288em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 0px; height: 0px; display: inline !important; float: none !important;" alt="" /></span><span class="mi" id="MathJax-Span-33" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006D.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 16px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span class="mi" id="MathJax-Span-34" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006F.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span class="mi" id="MathJax-Span-35" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0064.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 10px; height: 13px; display: inline !important; float: none !important;" alt="" /><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mtext" id="MathJax-Span-36" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/00A0.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.288em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 0px; height: 0px; display: inline !important; float: none !important;" alt="" /></span><span class="mi" id="MathJax-Span-37" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006D.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 16px; height: 9px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.291em; overflow: hidden; width: 0px; height: 1.121em;"></span></span></nobr></span> to stone <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-10-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-38" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 7.199em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 6.97em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.259em 1000em 2.687em -0.397em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-39" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mo" id="MathJax-Span-40" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0028.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -5px; width: 6px; height: 19px; display: inline !important; float: none !important;" alt="" /></span><span class="mi" id="MathJax-Span-41" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006A.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -4px; width: 8px; height: 16px; display: inline !important; float: none !important;" alt="" /></span><span class="mo" id="MathJax-Span-42" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.231em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/002B.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -2px; width: 13px; height: 13px; display: inline !important; float: none !important;" alt="" /></span><span class="msubsup" id="MathJax-Span-43" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.231em; margin: 0px; vertical-align: 0px;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.86em; height: 0px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.454em); top: -2.224em; left: 0.003em;"><span class="mi" id="MathJax-Span-44" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0061.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; top: -2.053em; left: 0.517em;"><span class="mi" id="MathJax-Span-45" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; font-size: 12.3796px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/283/0069.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 4px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span></span><span class="mo" id="MathJax-Span-46" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0029.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.117em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -5px; width: 6px; height: 19px; display: inline !important; float: none !important;" alt="" /></span><span class="mtext" id="MathJax-Span-47" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/00A0.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.288em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 0px; height: 0px; display: inline !important; float: none !important;" alt="" /></span><span class="mi" id="MathJax-Span-48" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006D.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 16px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span class="mi" id="MathJax-Span-49" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006F.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span class="mi" id="MathJax-Span-50" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0064.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 10px; height: 13px; display: inline !important; float: none !important;" alt="" /><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mtext" id="MathJax-Span-51" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/00A0.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.288em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 0px; height: 0px; display: inline !important; float: none !important;" alt="" /></span><span class="mi" id="MathJax-Span-52" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006D.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 16px; height: 9px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.35em; overflow: hidden; width: 0px; height: 1.238em;"></span></span></nobr></span> (since all stones lie on a circle). All frogs start their jump at stone <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-11-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-53" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.631em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.574em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.374em 1000em 2.401em -0.454em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-54" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mn" id="MathJax-Span-55" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0030.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 13px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.885em;"></span></span></nobr></span>, then each of them can jump as many steps as he wants. A frog will occupy a stone when he reach it, and he will keep jumping to occupy as much stones as possible. A stone is still considered ``occupied" after a frog jumped away. They would like to know which stones can be occupied by at least one of them. Since there may be too many stones, the frogs only want to know the sum of those stones' identifiers.</div></div></div><div class="vj_input" style="color: rgb(34, 34, 34); font-family: Verdana, Arial, sans-serif; font-size: 14px;"><p class="pst" style="margin-bottom: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 18pt; font-weight: bold; color: blue;">Input</p><div class="textBG" style="border-radius: 10px; padding: 10px; border: 2px dotted; font-family: "Times New Roman", Times, serif; font-size: 17px; background-color: rgb(234, 235, 255);">There are multiple test cases (no more than <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-12-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-56" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 1.145em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 1.088em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.374em 1000em 2.401em -0.454em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-57" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mn" id="MathJax-Span-58" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0032.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 8px; height: 12px; display: inline !important; float: none !important;" alt="" /><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0030.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 13px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.885em;"></span></span></nobr></span>), and the first line contains an integer <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-13-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-59" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.403em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.403em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.374em 1000em 2.401em -0.511em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-60" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mi" id="MathJax-Span-61" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0074.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 6px; height: 12px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.826em;"></span></span></nobr></span>, meaning the total number of test cases. For each test case, the first line contains two positive integer <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-14-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-62" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.688em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.631em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.511em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-63" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mi" id="MathJax-Span-64" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006E.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 11px; height: 9px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.591em;"></span></span></nobr></span> and <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-15-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-65" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.974em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.917em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.511em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-66" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mi" id="MathJax-Span-67" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006D.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 16px; height: 9px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.591em;"></span></span></nobr></span> - the number of frogs and stones respectively <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-16-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-68" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 13.424em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 13.024em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.088em 1000em 2.687em -0.397em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-69" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mo" id="MathJax-Span-70" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0028.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -5px; width: 6px; height: 19px; display: inline !important; float: none !important;" alt="" /></span><span class="mn" id="MathJax-Span-71" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0031.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 8px; height: 12px; display: inline !important; float: none !important;" alt="" /></span><span class="mo" id="MathJax-Span-72" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.288em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/2264.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.117em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -3px; width: 13px; height: 15px; display: inline !important; float: none !important;" alt="" /></span><span class="mi" id="MathJax-Span-73" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.288em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006E.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 11px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span class="mo" id="MathJax-Span-74" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.288em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/2264.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.117em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -3px; width: 13px; height: 15px; display: inline !important; float: none !important;" alt="" /></span><span class="msubsup" id="MathJax-Span-75" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.288em; margin: 0px; vertical-align: 0px;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 1.545em; height: 0px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.374em 1000em 2.401em -0.397em); top: -2.224em; left: 0.003em;"><span class="mn" id="MathJax-Span-76" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0031.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 8px; height: 12px; display: inline !important; float: none !important;" alt="" /><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0030.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 13px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; top: -2.681em; left: 1.088em;"><span class="mn" id="MathJax-Span-77" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; font-size: 12.3796px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/283/0034.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 6px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span></span><span class="mo" id="MathJax-Span-78" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/002C.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -4px; width: 4px; height: 6px; display: inline !important; float: none !important;" alt="" /></span><span class="mtext" id="MathJax-Span-79" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.174em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/00A0.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.288em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 0px; height: 0px; display: inline !important; float: none !important;" alt="" /></span><span class="mn" id="MathJax-Span-80" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0031.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 8px; height: 12px; display: inline !important; float: none !important;" alt="" /></span><span class="mo" id="MathJax-Span-81" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.288em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/2264.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.117em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -3px; width: 13px; height: 15px; display: inline !important; float: none !important;" alt="" /></span><span class="mi" id="MathJax-Span-82" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.288em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006D.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 16px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span class="mo" id="MathJax-Span-83" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.288em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/2264.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.117em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -3px; width: 13px; height: 15px; display: inline !important; float: none !important;" alt="" /></span><span class="msubsup" id="MathJax-Span-84" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.288em; margin: 0px; vertical-align: 0px;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 1.545em; height: 0px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.374em 1000em 2.401em -0.397em); top: -2.224em; left: 0.003em;"><span class="mn" id="MathJax-Span-85" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0031.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 8px; height: 12px; display: inline !important; float: none !important;" alt="" /><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0030.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 13px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; top: -2.681em; left: 1.088em;"><span class="mn" id="MathJax-Span-86" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; font-size: 12.3796px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/283/0039.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 6px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span></span><span class="mo" id="MathJax-Span-87" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0029.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.117em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -5px; width: 6px; height: 19px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.35em; overflow: hidden; width: 0px; height: 1.356em;"></span></span></nobr></span>. The second line contains <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-17-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-88" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.688em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.631em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.511em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-89" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mi" id="MathJax-Span-90" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/006E.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 11px; height: 9px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.591em;"></span></span></nobr></span> integers <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-18-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-91" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 5.942em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 5.771em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.63em -0.454em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-92" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-93" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.974em; height: 0px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.454em); top: -2.224em; left: 0.003em;"><span class="mi" id="MathJax-Span-94" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0061.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; top: -2.053em; left: 0.517em;"><span class="mn" id="MathJax-Span-95" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; font-size: 12.3796px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/283/0031.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 6px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span></span><span class="mo" id="MathJax-Span-96" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/002C.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -4px; width: 4px; height: 6px; display: inline !important; float: none !important;" alt="" /></span><span class="msubsup" id="MathJax-Span-97" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.174em; margin: 0px; vertical-align: 0px;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.974em; height: 0px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.454em); top: -2.224em; left: 0.003em;"><span class="mi" id="MathJax-Span-98" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0061.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; top: -2.053em; left: 0.517em;"><span class="mn" id="MathJax-Span-99" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; font-size: 12.3796px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/283/0032.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 6px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span></span><span class="mo" id="MathJax-Span-100" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/002C.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -4px; width: 4px; height: 6px; display: inline !important; float: none !important;" alt="" /></span><span class="mo" id="MathJax-Span-101" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.174em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/22EF.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 3px; width: 20px; height: 3px; display: inline !important; float: none !important;" alt="" /></span><span class="mo" id="MathJax-Span-102" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.174em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/002C.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -4px; width: 4px; height: 6px; display: inline !important; float: none !important;" alt="" /></span><span class="msubsup" id="MathJax-Span-103" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.174em; margin: 0px; vertical-align: 0px;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 1.031em; height: 0px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.454em); top: -2.224em; left: 0.003em;"><span class="mi" id="MathJax-Span-104" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0061.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; top: -2.053em; left: 0.517em;"><span class="mi" id="MathJax-Span-105" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; font-size: 12.3796px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/283/006E.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 8px; height: 6px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.291em; overflow: hidden; width: 0px; height: 0.826em;"></span></span></nobr></span>, where <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-19-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-106" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.917em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.86em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.573em -0.454em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-107" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-108" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.86em; height: 0px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.454em); top: -2.224em; left: 0.003em;"><span class="mi" id="MathJax-Span-109" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0061.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; top: -2.053em; left: 0.517em;"><span class="mi" id="MathJax-Span-110" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; font-size: 12.3796px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/283/0069.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 4px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.232em; overflow: hidden; width: 0px; height: 0.768em;"></span></span></nobr></span> denotes step length of the <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-20-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-111" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.403em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.403em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.374em 1000em 2.401em -0.511em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-112" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mi" id="MathJax-Span-113" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0069.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 6px; height: 13px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.056em; overflow: hidden; width: 0px; height: 0.885em;"></span></span></nobr></span>-th frog <span class="MathJax_Preview" style="color: rgb(136, 136, 136);"></span><span class="MathJax" id="MathJax-Element-21-Frame" role="textbox" aria-readonly="true" style="display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;"><nobr style="transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-114" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 6.913em;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 6.685em; height: 0px; font-size: 17.51px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.088em 1000em 2.687em -0.397em); top: -2.224em; left: 0.003em;"><span class="mrow" id="MathJax-Span-115" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><span class="mo" id="MathJax-Span-116" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0028.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -5px; width: 6px; height: 19px; display: inline !important; float: none !important;" alt="" /></span><span class="mn" id="MathJax-Span-117" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0031.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 8px; height: 12px; display: inline !important; float: none !important;" alt="" /></span><span class="mo" id="MathJax-Span-118" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.288em; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/2264.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.117em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -3px; width: 13px; height: 15px; display: inline !important; float: none !important;" alt="" /></span><span class="msubsup" id="MathJax-Span-119" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px 0px 0px 0.288em; margin: 0px; vertical-align: 0px;"><span style="transition: none; display: inline-block; position: relative; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0.86em; height: 0px;"><span style="transition: none; position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; clip: rect(1.602em 1000em 2.401em -0.454em); top: -2.224em; left: 0.003em;"><span class="mi" id="MathJax-Span-120" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Math/Italic/400/0061.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.003em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 9px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span><span style="transition: none; position: absolute; 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position: absolute; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; top: -2.681em; left: 1.088em;"><span class="mn" id="MathJax-Span-125" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; font-size: 12.3796px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/283/0039.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.06em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; width: 6px; height: 9px; display: inline !important; float: none !important;" alt="" /></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span></span><span class="mo" id="MathJax-Span-126" style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px;"><img src="http://acm.hdu.edu.cn/js/MathJax/fonts/HTML-CSS/TeX/png/Main/Regular/400/0029.png?rev=2.4-beta-2" style="max-width: none; transition: none; border: 0px; padding: 0px; margin: 0px 0.117em 0px 0px; max-height: none; min-width: 0px; min-height: 0px; vertical-align: -5px; width: 6px; height: 19px; display: inline !important; float: none !important;" alt="" /></span></span><span style="transition: none; display: inline-block; position: static; border: 0px; padding: 0px; margin: 0px; vertical-align: 0px; width: 0px; height: 2.23em;"></span></span></span><span style="transition: none; display: inline-block; position: static; border-width: 0px 0px 0px 0.003em; border-left-style: solid; border-color: initial; padding: 0px; margin: 0px; vertical-align: -0.35em; overflow: hidden; width: 0px; height: 1.356em;"></span></span></nobr></span>.</div></div><div class="vj_output" style="color: rgb(34, 34, 34); font-family: Verdana, Arial, sans-serif; font-size: 14px;"><p class="pst" style="margin-bottom: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 18pt; font-weight: bold; color: blue;">Output</p><div class="textBG" style="border-radius: 10px; padding: 10px; border: 2px dotted; font-family: "Times New Roman", Times, serif; font-size: 17px; background-color: rgb(234, 235, 255);">For each test case, you should print first the identifier of the test case and then the sum of all occupied stones' identifiers.</div></div><div class="vj_sampleInput" style="color: rgb(34, 34, 34); font-family: Verdana, Arial, sans-serif; font-size: 14px;"><p class="pst" style="margin-bottom: 0px; font-family: Arial, Helvetica, sans-serif; font-size: 18pt; font-weight: bold; color: blue;">Sample Input</p><div class="textBG" style="border-radius: 10px; padding: 10px; border: 2px dotted; font-family: "Times New Roman", Times, serif; font-size: 17px; background-color: rgb(234, 235, 255);"><pre style="white-space: pre-wrap; word-wrap: break-word;">32 129 103 6022 33 669 9681 40 48 32 64 16 96 42 72

Sample Output

Case #1: 42Case #2: 1170Case #3: 1872

#include<iostream>#include<stdio.h>#include<cstring>#include<algorithm>#include<math.h>using namespace std;#define maxn 10005#define LL __int64int gcd(int a,int b){    return b==0?a:gcd(b,a%b);}int factor[maxn];int num[maxn],vis[maxn];int main(){    int T,cas = 1;    scanf("%d",&T);    while(T--)    {        int n,m,cnt = 0;        memset(num,0,sizeof(num));        memset(vis,0,sizeof(vis));        scanf("%d%d",&n,&m);        for(int i=1; i<=(int)sqrt(m); i++)        {            if(m%i==0)            {                factor[cnt++] = i;                if(i*i!=m)                    factor[cnt++] = m/i;            }        }        sort(factor,factor+cnt);        while(n--)        {            int d; scanf("%d",&d);            int tmp = gcd(d,m);            for(int i=0; i<cnt; i++)            {                if(factor[i]%tmp==0)                    vis[i] = 1;            }        }        vis[cnt-1] = 0;        LL ans = 0;        for(int i=0; i<cnt; i++)        {            if(vis[i]!=num[i])            {                int t = (m-1)/factor[i];                ans += (LL) t*(t+1)/2*factor[i]*(vis[i]-num[i]);                t = vis[i]-num[i];                for(int j=i+1; j<cnt; j++)                {                    if(factor[j]%factor[i]==0)                        num[j] += t;                }            }        }        printf("Case #%d: %I64d\n",cas++,ans);    }    return 0;}