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 Get(char a, char b) {
  if (a != 'a' && b != 'a') return 'a';
  if (a != 'b' && b != 'b') return 'b';
  if (a != 'c' && b != 'c') return 'c';
  if (a != 'd' && b != 'd') return 'd';
}
int main() {
  std::ios_base::sync_with_stdio(0);
  int n, t;
  std::cin >> n >> t;
  std::string str1, str2, str3;
  std::cin >> str1 >> str2;
  int otl = 0;
  for (size_t i = 0; i < str1.size(); i++) {
    if (str1[i] != str2[i]) otl++;
  }
  if (otl == t) {
    for (size_t i = 0; i < str1.size(); i++) {
      if (str1[i] == str2[i])
        str3.push_back(str1[i]);
      else
        str3.push_back(Get(str1[i], str2[i]));
    }
  } else if (otl < t) {
    int need = t - otl;
    for (size_t i = 0; i < str1.size(); i++) {
      if (str1[i] == str2[i] && need) {
        str3.push_back(Get(str1[i], str1[i]));
        need--;
      } else if (str1[i] == str2[i])
        str3.push_back(str1[i]);
      else
        str3.push_back(Get(str1[i], str2[i]));
    }
  } else if (otl > t) {
    if (otl > t + t) {
      str3 = "-1";
      goto l1;
    }
    int q = 0;
    int f = 0;
    for (size_t i = 0; i < str1.size(); i++) {
      if (str1[i] == str2[i]) {
        str3.push_back(str1[i]);
      } else {
        if (q >= otl + otl - t - t)
          str3.push_back(Get(str1[i], str2[i]));
        else if (f == 0)
          str3.push_back(str1[i]);
        else if (f == 1)
          str3.push_back(str2[i]);
        f ^= 1;
        q++;
      }
    }
  }
l1:
  std::cout << str3;
  return 0;
}