Your task is to calculate a^(b^(exp))

a: provided in input,500 => a >= 0

b: provided in input,500 => b >= 0

exp=(nC0)^2 + (nC1)^2 + (nC2)^2 + ... + (nCn)^2

n: provided in input,500=>n>=0

Note: The Output for 0^0 should be 1.

nCr denotes n choose r.

As the answer can be too large , you need to output modulo 10^9+7.

Input

The first line of each input file contains number of test cases t(t<=1000).

Then follow a new line.

Then follow t lines, each containing 3 integers, (i.e. a b n  in order) each of them separated by a space.

Output

Output Contains t lines, ith line contains the answer of the ith test case.

Example

Input:
1
1 1 1

Output:
1

Explanation

In first test case, the Value of exp is 2, value of 1^(1^2) is 1,so output is 1.

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