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 $x, y \in S$, their bitwise-and $x \And y$ should be in $S$. 
• For any $x, y \in S$, their bitwise-or $x \mid y$ 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 $k, n$. ($1 \le k \le 7, 0 \le n \le 2^k$)

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 denoting the number of good sets.