Question

Str_ing

You are given N strings S1, S2,. ., SN as well as M strings T1, T2,. ., TM.

You have to create a string Y such that Y is a concatenation of a permutation of all N strings S1, S2,. ., SN separated by underscore (_). Length of Y should be between 3 and 16 inclusive and also Y should be constructed in such a way that it doesn’t match any of the M strings T1, T2,. ., TM.

If multiple answers are possible, output any string Y. If no such Y is possible, output -1

You have to create a string Y such that Y is a concatenation of a permutation of all N strings S1, S2,. ., SN separated by underscore (_). Length of Y should be between 3 and 16 inclusive and also Y should be constructed in such a way that it doesn’t match any of the M strings T1, T2,. ., TM.

If multiple answers are possible, output any string Y. If no such Y is possible, output -1

Input

The first line of the input contains a two integers N and M

The second line contains N strings S1, S2,. ., SN

The third line contains M strings T1, T2,. ., TM

Constraints:

1) 1 <= N <= 8

2) 0 <= M <= 10^5

3) N and M are integers.

4) 1 <= ∣Si∣ <= 16

5) N - 1 + ∑|Si| <= 16

6) Si != Sj if i != j.

7) Si is a string consisting of lowercase English letters.

8) 3 <= |Ti| <= 16

9) Ti != Tj if i != j.

10) Ti is a string consisting of lowercase English letters and _.

The second line contains N strings S1, S2,. ., SN

The third line contains M strings T1, T2,. ., TM

Constraints:

1) 1 <= N <= 8

2) 0 <= M <= 10^5

3) N and M are integers.

4) 1 <= ∣Si∣ <= 16

5) N - 1 + ∑|Si| <= 16

6) Si != Sj if i != j.

7) Si is a string consisting of lowercase English letters.

8) 3 <= |Ti| <= 16

9) Ti != Tj if i != j.

10) Ti is a string consisting of lowercase English letters and _.

Output

Output the answer string Y in a single line

Example

Sample Input 1:

2 2

newton school

newwton school_newton

Sample Output 1:

newton_school

Explanation 1:

Strings like newton_school and school_newton are possible but only newton_school can be considered because school_newton is already in the second list.

Sample Input 2:

2 2

newton school

school_newton newton_school

Sample Output 2:

-1

Sample Input 3:

4 4

ab cd ef gh

adsf fueh ____ ab_cd_ef_gh_

Sample Output 3:

ab_cd_ef_gh

2 2

newton school

newwton school_newton

Sample Output 1:

newton_school

Explanation 1:

Strings like newton_school and school_newton are possible but only newton_school can be considered because school_newton is already in the second list.

Sample Input 2:

2 2

newton school

school_newton newton_school

Sample Output 2:

-1

Sample Input 3:

4 4

ab cd ef gh

adsf fueh ____ ab_cd_ef_gh_

Sample Output 3:

ab_cd_ef_gh