Your task is to find a^expb,

a: Provided in input, 0 ≤ a ≤ 10⁵

b: Provided in Input, 0 ≤ b ≤ 10⁵

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

n: Provided in the input, 0 ≤ n ≤ 10⁵

As the answer can be too large, you need to output modulo 10⁹+7.

nCr denotes n choose r.

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 1²¹ is 1, so output is 1.

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