UVA 11880 Ball in a Rectanglefds

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运动问题，有边界，入射角等于出射角

所以x、y分别按周期变化

Description

Input: Standard Input Output: Standard Output

There is a rectangle on the cartesian plane, with bottom-left corner at (0,0) and top-right corner at (L, W). There is a ball centered at (x,y), with radius=R, shown below

$\epsfbox{p11880.eps}$

At time 0, the ball starts to move along a ray with polar angle a (the angle from positive x-axis to the ray, rotating counter-clockwise). When hitting the rectangle boundary, the reflex angle always equals to the incidence angle. The ball's velocity is always v (i.e. it never changes when hitting the rectangle). Where is the center of the ball at time s?

Input

There will be at most 25 test cases, each contains a line with 8 integers L, W, x, y, R, a, v, s ( 100 $\le$ L, W $\le$ 10⁹, 1 $\le$ R $\le$ 5, R $\le$ x $\le$ L - R, R $\le$ y $\le$ W - R, 0 $\le$ a < 360, 1 $\le$ v, s $\le$ 10⁹), as stated above. The input terminates with L = W = x = y = R = a = v = s = 0, which should not be processed.

Output

For each test case, output a line containing two floating-point numbers x, y, rounded to two decimal points, indicating that the center of ball will be at (x, y) at time s.

Sample Input

100 100 80 10 5 90 2 23110 100 70 10 5 180 1 99990 0 0 0 0 0 0 0

Sample Output

80.00 56.0071.00 10.00

Problemsetter: Rujia Liu, Special Thanks: Yiming Li, Shamim Hafiz & Sohel Hafiz

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