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New Year and Entity Enumeration

2000ms 262144K

Description:

You 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.

  1. If , then .
  2. If , then
  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 109 + 7.

Input:

The 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.

Output:

Print a single integer, the number of good sets modulo 109 + 7.

Sample Input:

5 3
11010
00101
11000

Sample Output:

4

Sample Input:

30 2
010101010101010010101010101010
110110110110110011011011011011

Sample Output:

860616440

Note:

An example of a valid set S is {00000, 00101, 00010, 00111, 11000, 11010, 11101, 11111}.

Informação

Codeforces

Provedor Codeforces

Código CF908E

Tags

bitmaskscombinatoricsdpmath

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Datas 09/05/2023 09:21:52

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