P9131 [USACO23FEB] Problem Setting P

题目描述

Note: The memory limit for this problem is 512MB, twice the default.

Farmer John created $N(1 \le N \le 10^5)$ problems. He then recruited $M (1 \le M \le 20)$ test-solvers, each of which rated every problem as "easy" or "hard."

His goal is now to create a problemset arranged in increasing order of difficulty, consisting of some subset of his $N$ problems arranged in some order. There must exist no pair of problems such that some test-solver thinks the problem later in the order is easy but the problem earlier in the order is hard.

Count the number of distinct nonempty problemsets he can form, modulo $10^9+7$.

输入格式

The first line contains $N$ and $M$.

The next $M$ lines each contain a string of length $N$. The $i$-th character of this string is E if the test-solver thinks the ith problem is easy, or H otherwise.

输出格式

The number of distinct problemsets FJ can form, modulo $10^9+7$.

输入输出样例 1

3 1
EHE

9

输入输出样例 2

10 6
EHEEEHHEEH
EHHHEEHHHE
EHEHEHEEHH
HEHEEEHEEE
HHEEHEEEHE
EHHEEEEEHE

33

说明/提示

Explanation for Sample 1

The nine possible problemsets are as follows:

$[1]$
$[1,2]$
$[1,3]$
$[1,3,2]$
$[2]$
$[3]$
$[3,1]$
$[3,2]$
$[3,1,2]$

Note that the order of the problems within the problemset matters.

SCORING

• Inputs $3-4$: $M=1$
• Inputs $5-14$: $M \le 16$
• Inputs $15-22$: No additional constraints.