Number Sequence

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

题解：打表找规律

感受：将for循环里面的1000换成maxn，会wrong，想不通。将for换成while也会wrong，懵逼!!!!!!

#pragma warning(disable:4996)
#include<map>
#include<string>
#include<cstdio>
#include<bitset>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;

const int maxn = 1005;

int a, b, n;
int F[maxn];

int main()
{
    F[1] = F[2] = 1;
    while (scanf("%d%d%d", &a, &b, &n) != EOF) {
        if (!a && !b && !n) break;
        int k;
        for (k = 3; k < 1000; k++) {
            F[k] = (a*F[k - 1] + b * F[k - 2]) % 7;
            if (F[k] == 1 && F[k - 1] == 1) break;
        }
        n = n % (k - 2);
        F[0] = F[k - 2];
        printf("%d
", F[n]);
    }
    return 0;
}