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