1829H · Don't Blame Me

Problem: 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 Format: 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 Format: 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 $10^9+7$.