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:
n,t=map(int,input().split())
r=input()
s=input()
u=len(s)
v=[]
for i in range(len(s)):
	if r[i]!=s[i]:v+=[i]
m=len(v)
if t>=m:
	j=t-m
	for i in range(u):
		if r[i]!=s[i]:
			if r[i]!='a' and s[i]!='a':print('a',end="")
			elif r[i]!='b' and s[i]!='b':print('b',end="")
			else:print('c',end="")
		elif j>0:
			j-=1
			if r[i]!='a' and s[i]!='a':print('a',end="")
			elif r[i]!='b' and s[i]!='b':print('b',end="")
			else:print('c',end="")
		else:print(s[i],end="")
elif m%2==0:
	k=m//2
	if t<k:print(-1)
	else:
		j=2*(t-k)
		jj=m-t
		for i in range(u):
			if r[i]==s[i]:print(s[i],end="")
			elif j>0:
				j-=1
				if r[i]!='a' and s[i]!='a':print('a',end="")
				elif r[i]!='b' and s[i]!='b':print('b',end="")
				else:print('c',end="")
			elif jj>0:
				jj-=1
				print(r[i],end="")
			else:
				print(s[i],end="")
else:
	k=(m-1)//2
	if t<=k:print(-1)
	else:
		t-=1
		j=2*(t-k)+1
		jj=2*k-t
		for i in range(u):
			if r[i]==s[i]:print(s[i],end="")
			elif j>0:
				j-=1
				if r[i]!='a' and s[i]!='a':print('a',end="")
				elif r[i]!='b' and s[i]!='b':print('b',end="")
				else:print('c',end="")
			elif jj>0:
				jj-=1
				print(r[i],end="")
			else:
				print(s[i],end="")