human
Can you provide a Python program to print the result modulo 1 000 000 007 (10^9 + 7) given the following:
PYTHON3 solution for "Moamen and Ezzat are playing a game. They create an array a of n non-negative integers where every element is less than 2^k.

Moamen wins if a_1  \&  a_2  \&  a_3  \&  …  \&  a_n ≥ a_1 ⊕ a_2 ⊕ a_3 ⊕ … ⊕ a_n.

Here \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND), and ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

Please calculate the number of winning for Moamen arrays a.

As the result may be very large, print the value modulo 1 000 000 007 (10^9 + 7).

Input

The first line contains a single integer t (1 ≤ t ≤ 5)— the number of test cases. 

Each test case consists of one line containing two integers n and k (1 ≤ n≤ 2⋅ 10^5, 0 ≤ k ≤ 2⋅ 10^5).

Output

For each test case, print a single value — the number of different arrays that Moamen wins with.

Print the result modulo 1 000 000 007 (10^9 + 7).

Example

Input

3
3 1
2 1
4 0

Output

5
2
1

Note

In the first example, n = 3, k = 1. As a result, all the possible arrays are [0,0,0], [0,0,1], [0,1,0], [1,0,0], [1,1,0], [0,1,1], [1,0,1], and [1,1,1].

Moamen wins in only 5 of them: [0,0,0], [1,1,0], [0,1,1], [1,0,1], and [1,1,1].":
assistant
#Here is Python program to print the result modulo 1 000 000 007 (10^9 + 7).
 def ksm(a, b, c=int(1e9+7)):
    if b == 0:
        return 1
    a = a%c
    res = 1
    while b:
        if b%2 == 1:
            res = res*a%c
        a = a*a%c
        b = b // 2
    return res

p = int(1e9+7)
mi = [1]
for i in range(211111):
    mi.append(mi[i]*2%p)
for _ in range(int(input())):
    n, k = map(int, input().split())
    if n % 2 == 1:
        da = 0
        den0 = ksm(2, n-1)
        den1 = 1
    else:
        da = 1
        den0 = ksm(2, n-1) - 1
        den1 = 0
    res = 0
    if n % 2 == 0:
        cz0 = 1
        cz1 = ksm(2, n)
        for i in range(1, k+1):
            res = (res + ksm(cz1, k-i)*cz0)%p
            cz0 = cz0*den0 % p
    res = (res + ksm(den1+den0, k))%p
    if k == 0:
        print(1)
    else:
        print(res)