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;
int main() {
  std::ios::sync_with_stdio(false);
  int n, t;
  cin >> n >> t;
  string s1, s2;
  cin >> s1 >> s2;
  int sim = 0, diff = 0;
  for (int i = 0; i < n; i++) {
    if (s1[i] == s2[i])
      sim++;
    else
      diff++;
  }
  if (diff <= t) {
    int change = t - diff;
    string ans = "";
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) {
        for (int j = 0; j < 26; j++) {
          char ch = 'a' + j;
          if (s1[i] != ch && s2[i] != ch) {
            ans += ch;
            break;
          }
        }
      } else {
        if (change <= 0) {
          ans += s1[i];
          continue;
        }
        change--;
        for (int j = 0; j < 26; j++) {
          char ch = 'a' + j;
          if (s1[i] != ch && s2[i] != ch) {
            ans += ch;
            break;
          }
        }
      }
    }
    cout << ans;
  } else {
    int finale = 0;
    for (int i = t; i >= 0; i--) {
      int support = (diff - i) * 2;
      if (support > diff) {
        cout << -1;
        return 0;
      }
      if (support % 2 != 0) continue;
      finale = i;
      break;
    }
    if (sim < t - finale) {
      cout << -1;
      return 0;
    }
    int change = t - finale;
    int support_one = diff - finale;
    int support_two = support_one;
    string ans = "";
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) {
        if (support_one > 0) {
          support_one--;
          ans += s1[i];
          continue;
        }
        if (support_two > 0) {
          support_two--;
          ans += s2[i];
          continue;
        }
        for (int j = 0; j < 26; j++) {
          char ch = 'a' + j;
          if (s1[i] != ch && s2[i] != ch) {
            ans += ch;
            break;
          }
        }
      } else {
        if (change <= 0) {
          ans += s1[i];
          continue;
        }
        change--;
        for (int j = 0; j < 26; j++) {
          char ch = 'a' + j;
          if (s1[i] != ch && s2[i] != ch) {
            ans += ch;
            break;
          }
        }
      }
    }
    cout << ans;
  }
  return 0;
}