E. New Year and Entity Enumerationtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an integer m.Let M = 2m - 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.   If , then .  If , then     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 109 + 7.InputThe first line will contain two integers m and n (1 ≤ m ≤ 1 000, 1 ≤ n ≤ min(2m, 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.OutputPrint a single integer, the number of good sets modulo 109 + 7. ExamplesInput5 3110100010111000Output4Input30 2010101010101010010101010101010110110110110110011011011011011Output860616440NoteAn example of a valid set S is {00000, 00101, 00010, 00111, 11000, 11010, 11101, 11111}.
Input5 3110100010111000
Output4
['bitmasks', 'combinatorics', 'dp', 'math', '*2500']