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:
#!/usr/bin/env python3
import collections, itertools, fractions, functools, heapq, math, queue, copy

def other(a, b):
  for c in 'abc':
    if c != a and c != b:
        return c

def solve():
  n, t = map(int, input().split())
  s1 = list(input())
  s2 = list(input())

  dif = sum(1 for a, b in zip(s1, s2) if a != b)
  if dif > 2*t:
      return -1

  s = []
  if dif <= t:
    for a, b in zip(s1, s2):
      if a == b:
        if dif < t:
          dif += 1
          s.append(other(a, b))
        else:
          s.append(a)
      else:
          s.append(other(a, b))
  else:
    diff1 = dif
    diff2 = dif
    for a, b in zip(s1, s2):
      if a == b:
          s.append(a)
          continue
      if diff1 > t:
          s.append(b)
          diff1 -= 1
          continue
      if diff2 > t:
          s.append(a)
          diff2 -= 1
          continue
      s.append(other(a, b))

  return str.join('', s)

if __name__ == '__main__':
  print(solve())