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:
#!/usr/bin/python

#
# This is surprisingly tricky. Stomped again.
#
import sys
from math import *

def Ni(): return tuple(map(int, raw_input().split()))

n, t = Ni()
s1 = raw_input()
s2 = raw_input()

needmatches = n - t
s1matches = 0
s2matches = 0
output = [None] * n

for i in range(n):
    if s1[i] == s2[i] and needmatches > 0:
        output[i] = s1[i]
        needmatches -= 1
    if needmatches == 0:
        break

def differs(a, b):
    for c in "abcdefghijklmnopqrstuvwxyz":
        if a != c and b != c:
            return c
    assert "should not be here"

for i in range(n):
    if output[i] != None:
        continue

    if s1[i] == s2[i]:
        if s1matches < needmatches and s2matches < needmatches:
            output[i] = s1[i]
            s1matches += 1
            s2matches += 1
        else:
            output[i] = differs(s1[i], s2[i])
    else:
        if s1matches < needmatches:
            output[i] = s1[i]
            s1matches += 1
        elif s2matches < needmatches:
            output[i] = s2[i]
            s2matches += 1
        else:
            output[i] = differs(s1[i], s2[i])

    #print output, s1matches, s2matches

if s1matches < needmatches or s2matches < needmatches:
    print -1
    sys.exit()

print "".join(output)