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

Note that in this task we assume that $0^0=1$.

Input

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

After 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