405979: GYM102201 G Good Set

Seunghyun is a mathematician, and he likes good jokes.

For a set U = {0, 1, ..., 2^k - 1}, a nonempty subset is good if it satisfies the following rules.

• for any , their bitwise-and should be in S.
• for any , their bitwise-or should be in S.

You are given n distinct integers in [0, 2^k - 1] range. Find the number of good sets which contains all n integers.

The first line contains two integers k, n. (1 ≤ k ≤ 7, 0 ≤ n ≤ 2^k)

The next line contains n distinct integers a₁, a₂, ..., a_n(0 ≤ a_i ≤ 2^k - 1).

Print a single integer denoting the number of good sets.

2 1
0

7

4 3
1 2 7

29