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()

def dc(s1, s2=None):
	if s2 == None:
		s2 = s1
	for i in 'abcd':
		if s1 != i and s2 != i:
			return i


def diffr(s1,s2):
	count = 0
	for i in xrange(len(s1)):
		if s1[i] != s2[i]:
			count+=1
	return count

d = diffr(s1,s2)
#print d
if t < (d+1)/2:
	print -1
	exit()

arr = [0 for i in xrange(n)]
if t < d:
	k = d-t
	d1 = 0
	d2 = 0
	for i in xrange(n):
		if s1[i] != s2[i]:
			if d1 < k:
				arr[i] = s2[i]
				d1 += 1
			elif d2 < k:
				arr[i] = s1[i]
				d2 += 1
			else:
				break

if t == d or t < d:
	for i in xrange(n):
		if s1[i]==s2[i]:
			arr[i] = s1[i]
		else:
			if arr[i] == 0:
				arr[i] = dc(s1[i], s2[i])
				
if t > d:
	dd = 0
	for i in xrange(n):
		if s1[i] != s2[i]:
			arr[i] = dc(s1[i], s2[i])
		else:
			if dd < t-d:
				arr[i] = dc(s1[i])
				dd+=1
			else:
				arr[i] = s1[i]
#print arr
print "".join(arr)