Your task is to calculate a^bexp.

• 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 input, 0 ≤ n ≤ 10⁵

Note: The output for 0⁰ should be 1.

nCr denotes n choose r.

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

Input

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

Then follows a new line.

Then follows 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 the first test case, the Value of exp is 2, value of 1¹² is 1, so output is 1.

Note: First try out the tutorial version where limits are low. POWRTU

Click here to see my set of problems at SPOJ.