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 dif(char c1, char c2) {
  char x = 'a';
  while (x == c1 || x == c2) x++;
  return x;
}
int main() {
  ios_base::sync_with_stdio(0);
  int n, t;
  cin >> n >> t;
  string s1, s2;
  cin >> s1 >> s2;
  int ig = 0, df = 0;
  for (int i = 0; i < n; i++) s1[i] == s2[i] ? ig++ : df++;
  if (n - t <= ig) {
    int mato = ig - (n - t);
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i]) {
        if (mato > 0) {
          cout << dif(s1[i], s2[i]);
          mato--;
        } else
          cout << s1[i];
      } else
        cout << dif(s1[i], s2[i]);
    }
    cout << endl;
    return 0;
  }
  int falta = (n - t) - ig;
  if (2 * falta > df) {
    cout << -1 << endl;
    return 0;
  }
  int cnt = 2 * falta;
  for (int i = 0; i < n; i++) {
    if (s1[i] == s2[i])
      cout << s1[i];
    else {
      if (cnt > 0) {
        if (cnt % 2 == 0) {
          cout << s1[i];
          cnt--;
        } else {
          cout << s2[i];
          cnt--;
        }
      } else {
        cout << dif(s1[i], s2[i]);
      }
    }
  }
  cout << endl;
  return 0;
}