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;
signed main() {
  long long n, t;
  cin >> n >> t;
  string a, b;
  cin >> a >> b;
  string ans;
  long long x = 0, k = n - t;
  for (long long i = 0; i < n; i++) {
    if (a[i] == b[i]) x++;
  }
  if (x >= k) {
    long long y = 0;
    for (long long i = 0; i < n; i++) {
      if (a[i] == b[i] && y < k) {
        ans += a[i];
        y++;
      } else {
        for (char ch = 'a'; ch <= 'z'; ch++) {
          if (ch != a[i] && ch != b[i]) {
            ans += ch;
            break;
          }
        }
      }
    }
    cout << ans;
  } else {
    long long rem = k - x;
    long long c = 0;
    if (2 * rem > n - x) {
      cout << "-1";
      c++;
    } else {
      long long y = 0;
      for (long long i = 0; i < n; i++) {
        if (a[i] == b[i])
          ans += a[i];
        else if (y >= 0 && y < rem) {
          ans += a[i];
          y++;
        } else if (y >= rem && y < 2 * rem) {
          ans += b[i];
          y++;
        } else {
          for (char ch = 'a'; ch <= 'z'; ch++) {
            if (ch != a[i] && ch != b[i]) {
              ans += ch;
              break;
            }
          }
        }
      }
    }
    if (!c) cout << ans;
  }
}