CSES - 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
• $1 \le n \le 10^5$
• $0 \le a,b,c \le 10^9$
Example

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

Output:
2187 50625 763327764