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 getOther(const char c1, const char c2) {
  for (char i = 97; i < 100; ++i) {
    if (i != c1 && i != c2) return i;
  }
  return 'z';
}
int main() {
  int n, t;
  string s1, s2;
  cin >> n >> t >> s1 >> s2;
  bool e = false;
  string ret(s1.length(), 'a');
  bool f = true;
  if (!t && s1 == s2) {
    ret = s1;
    e = true;
  }
  for (size_t i = 0; i < s1.length() && t; ++i) {
    if (s1[i] == s2[i])
      ret[i] = s1[i];
    else {
      ret[i] = f ? s1[i] : s2[i];
      if (!f) --t;
      f = !f;
    }
    if (!t) {
      e = true;
      for (size_t j = i + 1; j < s1.length(); ++j) {
        if (s1[j] != s2[j]) {
          e = false;
          break;
        }
        ret[j] = s1[j];
      }
      if (e) break;
    }
  }
  for (int i = s1.length() - 1; i >= 0 && t; --i) {
    if (s1[i] != s2[i]) {
      ret[i] = getOther(s1[i], s2[i]);
      if (!f) --t;
      f = !f;
    }
    if (!t) {
      e = true;
      break;
    }
  }
  for (size_t i = 0; i < s1.length() && t; ++i) {
    if (s1[i] == s2[i]) {
      ret[i] = getOther(s1[i], s2[i]);
      --t;
    }
    if (!t) {
      e = true;
      break;
    }
  }
  if (e)
    cout << ret;
  else
    cout << -1;
  return 0;
}