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

**Author: ***CHEN, Shunbao*