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;
char getDifferent(char a, char b) {
  char i = 'a';
  while (i == a || i == b) i++;
  return i;
}
int main() {
  int n, t;
  cin >> n >> t;
  string a, b;
  cin >> a;
  cin >> b;
  int diff = 0;
  string ans = "";
  for (int i = 0; i < a.length(); i++) {
    if (a[i] != b[i]) {
      diff++;
      ans.push_back('1');
    } else
      ans.push_back('0');
  }
  if (t * 2 < diff)
    cout << -1;
  else {
    int same = n - t;
    for (int i = 0; i < ans.length(); i++) {
      if (same > 0 && ans[i] == '0') {
        ans[i] = a[i];
        same--;
      }
      if (same == 0) break;
    }
    int f = 0;
    if (same > 0)
      for (int i = 0; i < ans.length(); i++) {
        if (same > 0 && ans[i] == '1') {
          if (f == 0) {
            ans[i] = a[i];
            f = 1 - f;
          } else {
            ans[i] = b[i];
            f = 1 - f;
            same--;
          }
        }
        if (same == 0) break;
      }
    for (int i = 0; i < ans.length(); i++)
      if (ans[i] == '0' || ans[i] == '1') {
        ans[i] = getDifferent(a[i], b[i]);
      }
    cout << ans << endl;
  }
  return 0;
}