B. Jzzhu and Sequences

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Jzzhu has invented a kind of sequences, they meet the following property:

You are given x and y, please calculate fn modulo 1000000007 (109 + 7).

Input

The first line contains two integers x and y (|x|, |y| ≤ 109). The second line contains a single integer n (1 ≤ n ≤ 2·109).

Output

Output a single integer representing fn modulo 1000000007 (109 + 7).

Sample test(s)

input

2 33

output

1

input

0 -12

output

1000000006

Note

In the first sample, f2 = f1 + f3, 3 = 2 + f3, f3 = 1.

In the second sample, f2 =  - 1;  - 1 modulo (109 + 7) equals (109 + 6).

解题说明：此题是一个数列求值，很显然用暴力计算超时，所以需要通过找规律来缩短时间。试验过后能发现数列的周期为6，这样题目就很容易了。

#include<iostream>#include<cstdio>#include<cmath>#include<algorithm>#include<cstdlib>#include<cstring>using namespace std;int F[10];int main() {int i, x, y, n, ans;scanf("%d %d", &x, &y);scanf("%d", &n);F[0] = x;F[1] = y;for (i = 1; i <= 6; ++i) {F[i+1] = (F[i] - F[i-1]) % 1000000007;}ans = (F[(n+5)%6] + 1000000007) % 1000000007;printf("%d\n", ans);return 0;}