H. Don't Blame Metime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputSadly, 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.InputEach 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.OutputFor 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.ExampleInput
65 11 1 1 1 14 00 1 2 35 15 5 7 4 21 2312 00 2 0 2 0 2 0 2 0 2 0 210 663 0 63 5 5 63 63 4 12 13Output
31
10
10
1
4032
15

65 11 1 1 1 14 00 1 2 35 15 5 7 4 21 2312 00 2 0 2 0 2 0 2 0 2 0 210 663 0 63 5 5 63 63 4 12 13
31 10 10 1 4032 15 
['bitmasks', 'combinatorics', 'dp', 'math', '*1700']