HDU-1005 Number Sequence

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

---

(a+b) mod c == (a mod c + b mod c) mod c

抽屉原理。

令［f(n-1), f(n-2)] 为一组，所以一共有 7*7 种不同的组合情况，到第 50 个时，一定会开始出现重复的组合，因为斐波那契数列 f(n) = f(n-1)+f(n-2)，所以开始循环重复，所以 7*7 为最大周期。

#include <iostream>
using namespace std;

int main(void)
{
    int a, b, n;
    int s[50];
    
    while(cin >> a >> b >> n && (a || b || n))
    {
        s[0] = 1; s[1] = 1;
        for(int i = 2; i < 49; i++)
        {
            s[i] = (a*s[i-1]+b*s[i-2]) % 7;
        }
        cout << s[n%49-1] << endl;
    }
    
    return 0;
}