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;
const int OO = 1e9;
const double EPS = 1e-9;
char diff(char c1, char c2) {
  for (char i = 97; i <= 122; i++) {
    if (i != c1 && i != c2) {
      return i;
    }
  }
  return -1;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, t;
  string s1, s2;
  cin >> n >> t >> s1 >> s2;
  int diff_c = 0;
  int eq_c = 0;
  for (int i = 0; i < n; i++) {
    if (s1[i] != s2[i]) {
      diff_c++;
    } else {
      eq_c++;
    }
  }
  int two_rem = (diff_c % 2 ? diff_c + 1 : diff_c) / 2;
  if (diff_c <= t && diff_c + eq_c >= t) {
    string ans = "";
    int eq_tb = t - diff_c;
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) {
        ans += diff(s1[i], s2[i]);
      } else {
        if (eq_tb > 0) {
          eq_tb--;
          ans += diff(s1[i], s2[i]);
        } else {
          ans += s1[i];
        }
      }
    }
    cout << ans << "\n";
  } else if (diff_c > t && two_rem <= t) {
    string ans = "";
    bool fs_taken = diff_c % 2;
    int y = 2 * (diff_c - t);
    int diff_s1 = 0;
    int diff_s2 = 0;
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) {
        if (y > 0) {
          if (diff_s1 >= diff_s2) {
            ans += s2[i];
            diff_s2++;
          } else {
            ans += s1[i];
            diff_s1++;
          }
          y--;
        } else {
          ans += diff(s1[i], s2[i]);
        }
      } else {
        ans += s1[i];
      }
    }
    cout << ans << "\n";
  } else {
    cout << "-1\n";
  }
  return 0;
}