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