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 output[100005];
char neither(char a, char b) {
  char output = 'a';
  while (output == a or output == b) output++;
  return output;
}
int main() {
  int n, t, mutuals = 0;
  string s1, s2;
  cin >> n >> t >> s1 >> s2;
  for (int i = 0; i < n; i++)
    if (s1[i] == s2[i]) mutuals++;
  if (t >= n - mutuals) {
    for (int i = 0; i < n and t != 0; i++) {
      if (s1[i] == s2[i]) continue;
      output[i] = neither(s1[i], s2[i]);
      t--;
    }
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) continue;
      if (t == 0)
        output[i] = s1[i];
      else {
        output[i] = neither(s1[i], s1[i]);
        t--;
      }
    }
  } else if (t >= (n - mutuals) / 2) {
    int switcher = 0, las = 0;
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i]) continue;
      if (switcher == 0)
        output[i] = s1[i];
      else
        output[i] = s2[i];
      switcher = (switcher + 1) % 2;
      las = i;
    }
    t -= (n - mutuals) / 2;
    if ((n - mutuals) % 2 == 1) {
      output[las] = neither(s1[las], s2[las]);
      t--;
    }
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) continue;
      if (t == 0)
        output[i] = s1[i];
      else {
        output[i] = neither(s1[i], s1[i]);
        t--;
      }
    }
    if (t > 0) {
      switcher = 0;
      for (int i = 0; i < n and t != 0; i++) {
        if (s1[i] == s2[i]) continue;
        output[i] = neither(s1[i], s2[i]);
        switcher++;
        if (switcher == 2) {
          switcher = 0;
          t--;
        }
      }
    }
  } else
    t = -1;
  if (t < 0)
    cout << -1;
  else
    cout << output;
  return 0;
}