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B. AND 0, Sum Big

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBaby 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 $$$10^9+7$$$.

Input

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 $$$k$$$ ($$$1 \le n \le 10^{5}$$$, $$$1 \le k \le 20$$$).

Output

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 $$$10^9+7$$$.

Example

Input

2 2 2 100000 20

Output

4 226732710

Note

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

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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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