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 PYTHON3):

Solution:
m = { chr(x) : chr(x + 1) for x in range(97,122) }
m['z'] = 'a'

n,t = map(int, input().split())
s1 = input()
s2 = input()
diffs = [True if s1[x] == s2[x] else False for x in range(n)]
same = diffs.count(True)
maximumDiffs = (n + same)//2

if t < n - maximumDiffs:
    print("-1")
else:
    newStr = []
    matchingCharsPerString = n - t

    c = matchingCharsPerString - same
    if c < 0:
        evenToCorrect = abs(c)
        for i,item in enumerate(diffs):
            if item:
                if evenToCorrect > 0:
                    newStr.append(m[s1[i]])
                    evenToCorrect -= 1
                else:
                    newStr.append(s1[i])
            else:
                candidate = m[s1[i]]
                if candidate == s2[i]:
                    candidate = m[s2[i]]
                newStr.append(candidate)
    else:
        matchesLeft = c
        toggle = True
        for i,item in enumerate(diffs):
            if item:
                    newStr.append(s1[i])
            else:
                if matchesLeft:
                    newStr.append( [s2[i],s1[i]][toggle])
                    toggle = not toggle
                    if toggle:
                        matchesLeft -= 1
                else:
                    candidate = m[s1[i]]
                    if candidate == s2[i]:
                        candidate = m[s2[i]]
                    newStr.append(candidate)
    print("".join(newStr))