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>
using namespace std;
int main() {
  int n, t, ok = 0;
  string s1, s2;
  cin >> n >> t >> s1 >> s2;
  t = n - t;
  for (int i = 0; i < n; i++) {
    if (s1[i] == s2[i]) ok++;
  }
  if (t <= ok) {
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i] && t > 0) {
        cout << s1[i];
        t--;
      } else if (s1[i] != 'a' && s2[i] != 'a')
        cout << 'a';
      else if (s1[i] != 'b' && s2[i] != 'b')
        cout << 'b';
      else
        cout << 'c';
    }
  } else if ((t - ok) * 2 > n - ok)
    cout << -1;
  else {
    ok = t - ok;
    t = ok * 2;
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i]) {
        cout << s1[i];
      } else if (t > ok) {
        cout << s1[i];
        t--;
      } else if (t > 0) {
        cout << s2[i];
        t--;
      } else if (s1[i] != 'a' && s2[i] != 'a')
        cout << 'a';
      else if (s1[i] != 'b' && s2[i] != 'b')
        cout << 'b';
      else
        cout << 'c';
    }
  }
  return 0;
}