—————————————1005————找规律的思想值得学习。

Problem Description
A number sequence is defined as follows:

f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7.

Given A, B, and n, you are to calculate the value of f(n).
 

Input
The input consists of multiple test cases. Each test case contains 3 integers A, B and n on a single line (1 <= A, B <= 1000, 1 <= n <= 100,000,000). Three zeros signal the end of input and this test case is not to be processed.
 

Output
For each test case, print the value of f(n) on a single line.
 

Sample Input
1 1 3
1 2 10
0 0 0
 

Sample Output
2
5
 

这一道题，很明显是一个找出答案的周期的题，其实这种题不能去写出来答案去观察，因为种类比较多，这个问题可以找出其中的变量和确定的量从而找出答案的循环周期。

 

 

 f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7.

在这里  递推的过程中,A,B的值是确定的，f[n-1]和f[n-2]的取值  都是只有七种，排列组合一下就有49种，这里关于数论的知识，在水题刷的差不多的话，就要去看书了，一定要看一点数论的书。