Problem: Marina loves strings of the same length and Vasya loves when there is a third string, different from them in exactly t characters. Help Vasya find at least one such string.

More formally, you are given two strings s1, s2 of length n and number t. Let's denote as f(a, b) the number of characters in which strings a and b are different. Then your task will be to find any string s3 of length n, such that f(s1, s3) = f(s2, s3) = t. If there is no such string, print  - 1.

Input

The first line contains two integers n and t (1 ≤ n ≤ 105, 0 ≤ t ≤ n).

The second line contains string s1 of length n, consisting of lowercase English letters.

The third line contain string s2 of length n, consisting of lowercase English letters.

Output

Print a string of length n, differing from string s1 and from s2 in exactly t characters. Your string should consist only from lowercase English letters. If such string doesn't exist, print -1.

Examples

Input

3 2
abc
xyc


Output

ayd

Input

1 0
c
b


Output

-1

Solution (in PYTHON):

Solution:
n,t = map(int,raw_input().split())
s1 = raw_input()
s2 = raw_input()

lowercase = 'abc'
equalPart = [s1[i]==s2[i] for i in xrange(n)]
#equalIndex = [i for i in xrange(n) if equalPart[i]]
#notequalIndex = [i for i in xrange(n) if not equalPart[i] ]
p=sum(equalPart) #number of parts that are equal

#think of the sameness rather than differentness

def findjunk(a,b):
    #a and b are two characters, find third unrelated characters
    if a != 'a' and b != 'a':
        return 'a'
    elif a != 'b' and b != 'b':
        return 'b'
    else:
        return 'c'

nbar = n-t# string that is the same
if 2*(nbar-p) > n-p:
    print -1
else:
    newstring=''
    if nbar<=p:
        equalIndexCounter=0
        for i in xrange(n):
            if equalPart[i] and equalIndexCounter<nbar: #copy the first part
                newstring += s1[i]
                equalIndexCounter +=1
            else:
                newstring += findjunk(s1[i], s2[i])
    else:
        notequalIndexCounter = 0
        for i in xrange(n):
            if equalPart[i]:
                newstring +=s1[i]
            elif notequalIndexCounter < nbar-p:
                newstring +=s1[i]
                notequalIndexCounter +=1
            elif  notequalIndexCounter < 2*(nbar-p):
                newstring +=s2[i]
                notequalIndexCounter +=1
            else:
                newstring +=findjunk(s1[i], s2[i])
    print newstring