CSES - Exponentiation
  • Time limit: 1.00 s
  • Memory limit: 512 MB
Your task is to efficiently calculate values $a^b$ modulo $10^9+7$.

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