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
INF = 10**20
MOD = 10**9 + 7
I = lambda:list(map(int,input().split()))
from math import gcd
from math import ceil
from collections import defaultdict as dd, Counter
from bisect import bisect_left as bl, bisect_right as br


"""
Facts and Data representation
Constructive? Top bottom up down
"""
n, k = I()
s = input()
t = input()

ans = list(s)
cnt = 0
idx = []
for i in range(n):
  if s[i] != t[i]:
    idx.append(i)
  else:
    ans[i] = s[i]

a = 'abcde'
ok = len(idx)
req = 0
for i in range(ok + 1):
  if (ok - i) % 2:
    continue
  count = i + (ok - i) // 2
  if count + n - ok >= k and count <= k:
    req = max(0, k - count)
    # print(k - count, count, i)
    for j in range(i):
      for ass in a:
        if ass != s[idx[j]] and ass != t[idx[j]]:
          ans[idx[j]] = ass
          break
    for j in range(i, ok):
      # print(j)
      if j % 2:
        ans[idx[j]] = s[idx[j]]
      else:
        ans[idx[j]] = t[idx[j]]
    break
else:
  print(-1)
  exit()

for i in range(n):
  if not req:
    break
  if s[i] == t[i]:
    if s[i] == 'a':
      ans[i] = 'z'
    else:
      ans[i] = 'a'
    req -= 1
print(''.join(ans))