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.

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.

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 _.

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.

见题面 Input 部分

见题面 Output 部分