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CSES Problem Set

Exponentiation II


Task | Statistics


CSES - Exponentiation IICSES - Exponentiation II

Time limit:1.00 s Memory limit:512 MB

Your task is to efficiently calculate values $a^{b^c}$ modulo $10^9+7$.

Input

The first input line has an integer $n$: the number of calculations.

Afther this, there are $n$ lines, each containing three integers $a$, $b$ and $c$.

Output

Print each value $a^{b^c}$ modulo $10^9+7$.

Constraints
Example

Input:
3
3 7 1
15 2 2
3 4 5


Output:
2187
50625
763327764