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:
import sys
import math
a=list(input().split(" "))
n=int(a[0])
t=int(a[1])
a=input()
b=input()
x=0
for i in range(n):
	if a[i]==b[i]:
		x+=1
if t<math.ceil((n-x)/2.0):
	print(-1)
	sys.exit()
ans=""
p=n-x-t
if p<0:
	p=0
q=t-p
r=t-n+x
if r<0:
	r=0
d=0
e=0
f=0
for i in range(n):
	if a[i]==b[i]:
		if f<r:
			if a[i]=='z':
				ans+='a'
			else:
				ans+='z'
			f+=1
		else:
			ans+=a[i]
	else:
		if e<2*p:
			if e%2==0:
				ans+=a[i]
			else:
				ans+=b[i]
			e+=1
		else:
			if a[i]=='a' or b[i]=='a':
				if a[i]=='b' or b[i]=='b':
					ans+='c'
				else:
					ans+='b'
			else:
				ans+='a'
			d+=1
print(ans)