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

a:provided in input,10^5=>a>=0

b:provided in input,10^5=>b>=0

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

n:provided in input,10^5=>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 conating 3 integers,(i.e a b n  in order) each of them seperated by a space.

Output

Output Contains t lines,ith line conatins 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.

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

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