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 31 2 100 0 0

Sample Output

25

解题报告：

f（n）对7求余，所以结果只有七种情况，再f（n）与f（n-1）和f（n-2）有关，f（n-1），f（n-2）最多有49种情况;所以可以用f（n%49）；

code：

#include<iostream>#include<algorithm>#include<stdio.h>#include<queue>#include<math.h>#include<string.h>#include<stdlib.h>using namespace std;int a,b,n;int f(int n){    if(n==1 || n==2)        return 1;    return ((a%7*f(n-1)%7)%7+(b%7*f(n-2)%7)%7)%7;  //求余公式，可以不用；}int main(){   // freopen("input.txt","r",stdin);    while(cin>>a>>b>>n&&a!=0&&b!=0&&n!=0){        cout<<f(n%49)<<endl;    }    return 0;}