102683: [AtCoder]ABC268 D - Unique Username

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.
• 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.

Sample Input 1

1 1
chokudai
chokudai

Sample Output 1

-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.

Sample Input 2

2 2
choku
dai
chokudai
choku_dai

Sample Output 2

dai_choku

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

Sample Input 3

2 2
chokudai
atcoder
chokudai_atcoder
atcoder_chokudai

Sample Output 3

-1

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

Sample Input 4

4 4
ab
cd
ef
gh
hoge
fuga
____
_ab_cd_ef_gh_

Sample Output 4

ab__ef___cd_gh

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

问题描述

高桥凉介正在为一个服务决定用户名，但遇到了困难。编写一个代码来帮助他。

找到一个满足以下所有条件的字符串$X$：

• $X$是通过以下过程获得的：
  • 将$S_1, S_2, \ldots,S_N$排列为$S_1', S_2', \ldots,S_N'$。将$S_1'$，（1个或多个_），$S_2'$，（1个或多个_），$\ldots$，（1个或多个_），和$S_N'$按此顺序连接起来。
• $X$的长度在3到16之间（含3和16）。
• $X$不与任何字符串$T_1,T_2,\ldots,T_M$相等。

如果没有满足所有条件的$X$，则打印-1。

约束条件

• $1 \leq N \leq 8$
• $0 \leq M \leq 10^5$
• $N$和$M$是整数。
• $1 \leq |S_i| \leq 16$
• $N-1+\sum{|S_i|} \leq 16$
• 如果$i \neq j$，则$S_i \neq S_j$。
• $S_i$是一个由小写英文字母组成的字符串。
• $3 \leq |T_i| \leq 16$
• 如果$i \neq j$，则$T_i \neq T_j$。
• $T_i$是一个由小写英文字母和_组成的字符串。

输入

输入通过标准输入给出，格式如下：

$N$ $M$
$S_1$
$S_2$
$\vdots$
$S_N$
$T_1$
$T_2$
$\vdots$
$T_M$

输出

打印一个满足所有条件的字符串$X$。如果没有满足所有条件的$X$，则打印-1。
如果有多个解，打印其中任何一个即可。

样例输入1

1 1
chokudai
chokudai

样例输出1

-1

满足第一和第二个条件的唯一字符串是$X=$ chokudai，但它与$T_1$相等。
因此，没有满足所有条件的$X$，因此应该打印-1。

样例输入2

2 2
choku
dai
chokudai
choku_dai

样例输出2

dai_choku

像choku__dai（在choku和dai之间有两个_）这样的字符串也满足所有条件。

样例输入3

2 2
chokudai
atcoder
chokudai_atcoder
atcoder_chokudai

样例输出3

-1

chokudai__atcoder和atcoder__chokudai（在chokudai和atcoder之间有两个_）的长度为17，违反了第二个条件。

样例输入4

4 4
ab
cd
ef
gh
hoge
fuga
____
_ab_cd_ef_gh_

样例输出4

ab__ef___cd_gh

给定的$T_i$可能包含一个不能通过第一个条件中描述的过程获得的字符串。