hdu 3579:Hello Kiki (线性同余方程组求正整数解)

                                                             Hello Kiki

Problem Description

Hello Kiki is such a lovely girl that she loves doing counting in a different way. For example, when she is counting X coins, she count them N times. Each time she divide the coins into several same sized groups and write down the group size Mi and the number of the remaining coins Ai on her note.
One day Kiki's father found her note and he wanted to know how much coins Kiki was counting.

 

Input

The first line is T indicating the number of test cases.
Each case contains N on the first line, Mi(1 <= i <= N) on the second line, and corresponding Ai(1 <= i <= N) on the third line.
All numbers in the input and output are integers.
1 <= T <= 100, 1 <= N <= 6, 1 <= Mi <= 50, 0 <= Ai < Mi

 

Output

For each case output the least positive integer X which Kiki was counting in the sample output format. If there is no solution then output -1.

 

Sample Input

2214 575 56519 54 40 24 8011 2 36 20 76

 

Sample Output

Case 1: 341
Case 2: 5996

解题思路：参考poj 2891 Strange Way To Express Integers(线性同余方程组)，题目链接

http://blog.csdn.net/u012717411/article/details/43016705

注意0<=A[i]，A[i]可均为0，即X可能为零，这在许多问题中是不会出现的，在这里是个坑。。。。。要特判一下

参考代码：