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 differ(char a, char b) {
  for (int i = 0; i < 3; i++)
    if ('a' + i != a && 'a' + i != b) return 'a' + i;
}
int main() {
  int n, t;
  string s1, s2;
  cin >> n >> t >> s1 >> s2;
  int dif = 0;
  for (int i = 0; i < n; i++)
    if (s1[i] != s2[i]) dif++;
  int same = n - dif;
  if ((dif + 1) / 2 > t)
    cout << -1;
  else {
    string res = "";
    int ds;
    int conc;
    if (t >= dif) {
      ds = t - dif;
      int nowd = 0;
      for (int i = 0; i < n; i++)
        if (s1[i] == s2[i]) {
          if (nowd < ds) {
            res += differ(s1[i], s2[i]);
            nowd++;
          } else
            res += s1[i];
        } else
          res += differ(s1[i], s2[i]);
    } else {
      conc = (dif - t) * 2;
      int nowd = 0;
      int id = -1;
      for (int i = 0; i < n; i++) {
        if (s1[i] == s2[i])
          res += s1[i];
        else if (nowd < conc) {
          if (id == -1) {
            id = i;
            res += s1[i];
          } else {
            res += s2[i];
            id = -1;
          }
          nowd++;
        } else {
          res += differ(s1[i], s2[i]);
        }
      }
    }
    cout << res;
  }
}