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 CPP):

Solution:
#include <bits/stdc++.h>
char min(char a, char b) { return (a < b ? a : b); }
char max(char a, char b) { return (a > b ? a : b); }
char diff(char a, char b) {
  if (max(a, b) != 'z') {
    return 'z';
  }
  if (min(a, b) != 'y') {
    return 'y';
  }
  return 'x';
}
int main() {
  int i, n, m;
  scanf("%d %d", &n, &m);
  m = n - m;
  char a[n + 1];
  char b[n + 1];
  char z[n + 1];
  memset(z, 0, (n + 1) * sizeof(char));
  scanf("%s", a);
  scanf("%s", b);
  for (i = 0; i < n; ++i) {
    if (a[i] == b[i]) {
      --m;
      if (m < 0) {
        break;
      }
      z[i] = a[i];
    }
  }
  int m2 = m;
  for (i = 0; i < n; ++i) {
    if (0 == z[i]) {
      if (m > 0) {
        z[i] = a[i];
        --m;
      } else if (m2 > 0) {
        z[i] = b[i];
        --m2;
      } else {
        z[i] = diff(a[i], b[i]);
      }
    }
  }
  if (m > 0 || m2 > 0) {
    printf("-1\n");
    return 0;
  }
  z[n] = '\0';
  printf("%s\n", z);
  return 0;
}