Exponentiation

Your task is to efficiently calculate values a^b modulo 10^9+7. Note that in this task we assume that 0^0=1.

Input

The first input line contains an integer n: the number of calculations. After this, there are n lines, each containing two integers a and b.

Output

Print each value a^b modulo 10^9+7.

Constraints

$1 \le n \le 2$ \cdot 10^5$

$0 \le a,b \le 10^9$

Example

Input

3
3 4
2 8
123 123

Output

81
256
921450052