CF1514B.AND 0, Sum Big

Baby Badawy's first words were "AND 0 SUM BIG", so he decided to solve the following problem. Given two integers $n$ and $k$ , count the number of arrays of length $n$ such that:

• all its elements are integers between $0$ and $2^k-1$ (inclusive);
• the bitwise AND of all its elements is $0$ ;
• the sum of its elements is as large as possible.

Since the answer can be very large, print its remainder when divided by $10^9+7$ .

The first line contains an integer $t$ ( $1 \le t \le 10$ ) — the number of test cases you need to solve.

Each test case consists of a line containing two integers $n$ and $k$ ( $1 \le n \le 10^{5}$ , $1 \le k \le 20$ ).

For each test case, print the number of arrays satisfying the conditions. Since the answer can be very large, print its remainder when divided by $10^9+7$ .

In the first example, the $4$ arrays are:

• $[3,0]$ ,
• $[0,3]$ ,
• $[1,2]$ ,
• $[2,1]$ .