A11547 | New Year and Entity Enumeration

You are given an integer $m$ .

Let $M=2^{m}-1$ .

You are also given a set of $n$ integers denoted as the set $T$ . The integers will be provided in base 2 as $n$ binary strings of length $m$ .

A set of integers $S$ is called "good" if the following hold.

1. If , then .
2. If , then 
3. 
4. All elements of $S$ are less than or equal to $M$ .

Here,  and  refer to the bitwise XOR and bitwise AND operators, respectively.

Count the number of good sets $S$ , modulo $10^{9}+7$ .

The first line will contain two integers $m$ and $n$ ( $1<=m<=1000$ , $1<=n<=min(2^{m},50)$ ).

The next $n$ lines will contain the elements of $T$ . Each line will contain exactly $m$ zeros and ones. Elements of $T$ will be distinct.

Print a single integer, the number of good sets modulo $10^{9}+7$ .