Good Set

Seunghyun is a mathematician, and he likes good jokes.

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

• For any $x, y \in A$, their bitwise AND $x \land y$ is in $A$.
• For any $x, y \in A$, their bitwise OR $x \lor y$ is in $A$.

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

The first line contains two integers $k$ and $n$ ($1 \le k \le 7$, $0 \le n \le 2^k$).

The next line contains $n$ distinct integers $a_1, a_2, \cdots, a_n$ ($0 \le a_i \le 2^k - 1$).

Print a single integer, the number of good sets.