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 inf = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
int main() {
  int n, k;
  cin >> n >> k;
  string s, t;
  cin >> s >> t;
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    if (s[i] == t[i]) {
      cnt++;
    }
  }
  if (k < (n - cnt) / 2 + (n - cnt) % 2) {
    cout << -1 << endl;
  } else {
    if (k <= (n - cnt)) {
      int x = ((n - cnt) - k) * 2;
      for (int i = 0; i < n; i++) {
        if (s[i] == t[i])
          cout << s[i];
        else {
          if (x) {
            if (x % 2) {
              cout << s[i];
              x--;
            } else
              cout << t[i], x--;
          } else {
            for (int j = 0; j < 26; j++) {
              char ch = j + 'a';
              if (ch != s[i] && ch != t[i]) {
                cout << ch;
                break;
              }
            }
          }
        }
      }
    } else {
      int x = k - (n - cnt);
      for (int i = 0; i < n; i++) {
        if (s[i] == t[i]) {
          if (x) {
            for (int j = 0; j < 26; j++) {
              char ch = j + 'a';
              if (ch != s[i]) {
                cout << ch;
                break;
              }
            }
            x--;
          } else
            cout << s[i];
        } else {
          for (int j = 0; j < 26; j++) {
            char ch = j + 'a';
            if (ch != s[i] && ch != t[i]) {
              cout << ch;
              break;
            }
          }
        }
      }
    }
  }
  return 0;
}