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:
import sys
n,t=map(int,sys.stdin.readline().split())
s1=sys.stdin.readline()
s2=sys.stdin.readline()
same=0
def diff(c1,c2):
  if 'a'!=c1 and 'a'!=c2:return 'a'
  if 'b'!=c1 and 'b'!=c2:return 'b'
  if 'c'!=c1 and 'c'!=c2:return 'c'
for i in range(n): 
 if s1[i]==s2[i]:same+=1

t3=n-t
if t3>((n-same)/2+same):print -1
else:
  t1=t3-same
  t2=t3-same
  for i in range(n):
    if s1[i]==s2[i]:
      if t3>0:
        t3-=1
        sys.stdout.write(s1[i])
      else:
        sys.stdout.write(diff(s1[i],s2[i]))
    else:
      if t1>0:
        t1-=1
        sys.stdout.write(s1[i])
      elif t2>0:
        t2-=1
        sys.stdout.write(s2[i])
      else:
        sys.stdout.write(diff(s1[i],s2[i]))
  print