(ℓ, d) pattern

You are given $k$ strings $S_1, S_2, \dots, S_k$. Every character in them is a space or one of the 26 lowercase letters a to z.

For two constants $\ell$ and $d$, compute an $(\ell, d)$-pattern of this set of strings. An $(\ell, d)$-pattern is a string $W = W[1]W[2] \cdots W[\ell]$ of length $\ell$ that satisfies the following property.

• For every $i = 1, 2, \dots, k$, the string $S_i$ contains at least one substring $X = X[1]X[2] \cdots X[\ell]$ of length $\ell$ whose Hamming distance from $W$ is at most $d$.

The Hamming distance between $X$ and $W$ is the number of positions $j$ with $X[j] \neq W[j]$. A substring is $\ell$ consecutive characters, and it may contain a space.

$W$ consists of lowercase letters only. The input is always such that exactly one $(\ell, d)$-pattern exists.

The first line contains two integers $\ell$ and $d$ separated by a space. ($1 \le \ell \le 10$, $0 \le d \le 2$)

The second line contains the number of strings $k$. ($1 \le k \le 30$)

Each of the next $k$ lines contains one string, in the order $S_1, S_2, \dots, S_k$. Each string has length at most 50 and uses only spaces and lowercase letters. A pattern exists, so every string has length at least $\ell$.

Print the $(\ell, d)$-pattern $W$ on the first line.