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

 

找循环，因为是对七取余，所以结果也就是0  1  2  3  4  5  6        7种，最少其次，即  7*7 = 49 种，循环节不一定以  1   1  开头。

#include <stdio.h>
#include <string.h>
#define pi 3.1415927

int sz[60];
int main()
{
int a,b,n,i,j,xc,xj,bj;

while(~scanf("%d%d%d",&a,&b,&n))
{
bj = 0;
sz[0] = 1;
sz[1] = 1;
sz[2] = 1;
if(a == 0 && b == 0 && n == 0)
break;
for(i = 3; i<=n && bj == 0; i++)
{
sz[i] =  (a * sz[i - 1] + b * sz[i - 2]) % 7;
for(j = 2; j<i; j++)
{
if(sz[j] == sz[i] && sz[j-1] == sz[i-1])
{
xc = j;
xj = i;
bj = 1;
break;
}
}
}
if(bj == 1)
printf("%d\n",sz[xc + (n - xj) % (xj - xc)]);
else
printf("%d\n",sz
);
}
return 0;
}