Crazy Malvika discovers Crazy Fibonacci function

Malvika was getting bored of the usual Fibonacci problems, and decided to add a little twist to it. She defined a new function f() with the following properties:

  • She'll give you two integers, A and Bf(1) is defined to be A and f(2) is B.
  • And for all integers x ≥ 2, f(x) = f(x-1) + f(x+1).

She'll give an integer N, and you have to find out what f(N) is. Output the answers modulo 109+7.

Input

  • The first line of input contains a single integer T denoting number of test cases.
  • The only line of each test case contains three integers: AB and N, denoting f(1)f(2) and the query.

Output

  • For each test case, output a line which contains a single integer, corresponding to f(N) for the given input.

Constraints

  • 1 ≤ T ≤ 105
  • -109 ≤ A , B ≤ 109
  • 1 ≤ N ≤ 109

Example

Input:
2
10 17 3
23 17 3


Output:
7
1000000001

Explanation

In the first test case, f(3) = 7, and so that is the output.

In the second test case, f(3) = -6 and the answer modulo 109+7 is 1000000001.

Author: Zohan
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