Moamen and XOR

2000ms

262144K

Description:

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 $$$a_1 \,\&\, a_2 \,\&\, a_3 \,\&\, \ldots \,\&\, a_n \ge a_1 \oplus a_2 \oplus a_3 \oplus \ldots \oplus a_n$$$.

Here $$$\&$$$ denotes the bitwise AND operation, and $$$\oplus$$$ denotes the bitwise XOR operation.

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 $$$t$$$ ($$$1 \le t \le 5$$$)— the number of test cases.

Each test case consists of one line containing two integers $$$n$$$ and $$$k$$$ ($$$1 \le n\le 2\cdot 10^5$$$, $$$0 \le k \le 2\cdot 10^5$$$).

Output:

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

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

Sample Input:

Sample 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 $$$[1,1,1]$$$.

Informação

Provedor Codeforces

Código CF1557C