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, k = map(int, input().split())
a = input()
b = input()
cnt = 0
for i in range(n):
  if (a[i] == b[i]):
    cnt += 1
dif = n - cnt
ok = n - (cnt + dif // 2)
if (k < ok):
  print(-1)
else:
  res, cur, req, i, nxt = {}, 0, n - k, 0, True
  while (cur < req):
    if (a[i] == b[i]):
      res[i], cur = a[i], cur + 1
    elif (nxt):
      pos, nxt = i, not nxt
    else:
      res[pos], res[i], nxt, cur = a[pos], b[i], not nxt, cur + 1
    i += 1
  if (nxt == False):
    if (('a' != a[pos]) and ('a' != b[pos])):
      res[pos] = 'a'
    elif (('b' != a[pos]) and ('b' != b[pos])):
      res[pos] = 'b'    
    elif (('c' != a[pos]) and ('c' != b[pos])):
      res[pos] = 'c' 
    else:
      res[pos] = 'd'
  while (i < n):
    if (('a' != a[i]) and ('a' != b[i])):
      res[i] = 'a'
    elif (('b' != a[i]) and ('b' != b[i])):
      res[i] = 'b'    
    elif (('c' != a[i]) and ('c' != b[i])):
      res[i] = 'c' 
    else:
      res[i] = 'd'
    i += 1
  for i in range(n):
    print(res[i], end = '')