Exponentiation II

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