Score : $400$ points

Problem Statement

Takahashi is having trouble with deciding a username for a service. Write a code to help him.

Find a string $X$ that satisfies all of the following conditions:

• $X$ is obtained by the following procedure:- Let $S_1', S_2', \ldots,S_N'$ be a permutation of $S_1, S_2, \ldots,S_N$. Let $X$ be the concatenation of $S_1'$, ($1$ or more copies of _), $S_2'$, ($1$ or more copies of _), $\ldots$, ($1$ or more copies of _), and $S_N'$, in this order.
• Let $S_1', S_2', \ldots,S_N'$ be a permutation of $S_1, S_2, \ldots,S_N$. Let $X$ be the concatenation of $S_1'$, ($1$ or more copies of _), $S_2'$, ($1$ or more copies of _), $\ldots$, ($1$ or more copies of _), and $S_N'$, in this order.
• The length of $X$ is between $3$ and $16$, inclusive.
• $X$ does not coincide with any of $M$ strings $T_1,T_2,\ldots,T_M$.

If there is no $X$ that satisfies all of the conditions, print -1 instead.

Constraints

• $1 \leq N \leq 8$
• $0 \leq M \leq 10^5$
• $N$ and $M$ are integers.
• $1 \leq |S_i| \leq 16$
• $N-1+\sum{|S_i|} \leq 16$
• $S_i \neq S_j$ if $i \neq j$.
• $S_i$ is a string consisting of lowercase English letters.
• $3 \leq |T_i| \leq 16$
• $T_i \neq T_j$ if $i \neq j$.
• $T_i$ is a string consisting of lowercase English letters and _.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$S_1$

$S_2$

$\vdots$

$S_N$

$T_1$

$T_2$

$\vdots$

$T_M$

Output

Print a string $X$ that satisfies all of the conditions. If there is no $X$ that satisfies all of the conditions, print -1 instead. If there are multiple solutions, print any of them.

1 1
chokudai
chokudai

-1

The only string that satisfies the first and second conditions is $X=$ chokudai, but it coincides with $T_1$. Thus, there is no $X$ that satisfies all of the conditions, so -1 should be printed.

2 2
choku
dai
chokudai
choku_dai

dai_choku

Strings like choku__dai (which has two _'s between choku and dai) also satisfy all of the conditions.

2 2
chokudai
atcoder
chokudai_atcoder
atcoder_chokudai

-1

chokudai__atcoder and atcoder__chokudai (which have two _'s between chokudai and atcoder) have a length of $17$, which violates the second condition.

4 4
ab
cd
ef
gh
hoge
fuga
____
_ab_cd_ef_gh_

ab__ef___cd_gh

The given $T_i$ may contain a string that cannot be obtained by the procedure described in the first condition.