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Don't Blame Me

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Description:

Sadly, the problem setter couldn't think of an interesting story, thus he just asks you to solve the following problem.

Given an array $$$a$$$ consisting of $$$n$$$ positive integers, count the number of non-empty subsequences for which the bitwise $$$\mathsf{AND}$$$ of the elements in the subsequence has exactly $$$k$$$ set bits in its binary representation. The answer may be large, so output it modulo $$$10^9+7$$$.

Recall that the subsequence of an array $$$a$$$ is a sequence that can be obtained from $$$a$$$ by removing some (possibly, zero) elements. For example, $$$[1, 2, 3]$$$, $$$[3]$$$, $$$[1, 3]$$$ are subsequences of $$$[1, 2, 3]$$$, but $$$[3, 2]$$$ and $$$[4, 5, 6]$$$ are not.

Note that $$$\mathsf{AND}$$$ represents the bitwise AND operation.

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case consists of two integers $$$n$$$ and $$$k$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$, $$$0 \le k \le 6$$$) — the length of the array and the number of set bits that the bitwise $$$\mathsf{AND}$$$ the counted subsequences should have in their binary representation.

The second line of each test case consists of $$$n$$$ integers $$$a_i$$$ ($$$0 \leq a_i \leq 63$$$) — the array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, output a single integer — the number of subsequences that have exactly $$$k$$$ set bits in their bitwise $$$\mathsf{AND}$$$ value's binary representation. The answer may be large, so output it modulo $$$10^9+7$$$.

Sample Input:

6
5 1
1 1 1 1 1
4 0
0 1 2 3
5 1
5 5 7 4 2
1 2
3
12 0
0 2 0 2 0 2 0 2 0 2 0 2
10 6
63 0 63 5 5 63 63 4 12 13

Sample Output:

31
10
10
1
4032
15

Informação

Codeforces

Provedor Codeforces

Código CF1829H

Tags

bitmaskscombinatoricsdpmath

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Datas 09/05/2023 10:39:31

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