You bought 3 ancient scrolls from a magician. These scrolls have a long string, and the lengths of the strings are the same. He said that these scrolls are copies of the key string to enter a dungeon with a secret treasure. However, he also said, they were copied so many times by hand, so the string will contain some errors, though the length seems correct.</p>

Your job is to recover the original string from these strings. When finding the original string, you decided to use the following assumption.

• The copied string will contain at most d errors. In other words, the Hamming distance of the original string and the copied string is at most d.
• If there exist many candidates, the lexicographically minimum string is the original string.

Can you find the orignal string?

입력 형식

The input contains a series of datasets.</p>

Each dataset has the following format:

l d
str1
str2
str3

The first line contains two integers (l) ((1 \leq l \leq 100,000)) and (d) ((0 \leq d \leq 5,000).) (l) describes the length of 3 given strings and (d) describes acceptable maximal Hamming distance. The following 3 lines have given strings, whose lengths are (l). These 3 strings consist of only lower and upper case alphabets.

The input ends with a line containing two zeros, which should not be processed.

출력 형식

Print the lexicographically minimum satisfying the condition in a line. If there do not exist such strings, print -1.

예제 입력

3 1
ACM
IBM
ICM
5 2
iwzwz
iziwi
zwizi
1 0
A
B
C
10 5
jLRNlNyGWx
yyLnlyyGDA
yLRnvyyGDA
0 0

예제 출력

ICM
iwiwi
-1
AARAlNyGDA