Score : $300$ points

Problem Statement

You are given $N$ strings $S_1,S_2,\dots,S_N$ consisting of lowercase English alphabets.

Consider choosing some number of strings from $S_1,S_2,\dots,S_N$.

Find the maximum number of distinct alphabets that satisfy the following condition: "the alphabet is contained in exactly $K$ of the chosen strings."

Constraints

• $1 \le N \le 15$
• $1 \le K \le N$
• $N$ and $K$ are integers.
• $S_i$ is a non-empty string consisting of lowercase English alphabets.
• For each integer $i$ such that $1 \le i \le N$, $S_i$ does not contain two or more same alphabets.
• If $i \neq j$, then $S_i \neq S_j$.

Input

Input is given from Standard Input in the following format:

$N$ $K$

$S_1$

$S_2$

$\vdots$

$S_N$

Output

Print the answer.

4 2
abi
aef
bc
acg

3

When $S_1,S_3$, and $S_4$ are chosen, a,b, and c occur in exactly two of the strings.

There is no way to choose strings so that $4$ or more alphabets occur in exactly $2$ of the strings, so the answer is $3$.

2 2
a
b

0

You cannot choose the same string more than once.

5 2
abpqxyz
az
pq
bc
cy

7