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;
void solve() {
  int n, t;
  cin >> n >> t;
  string a, b;
  cin >> a >> b;
  string ans = "";
  vector<int> match, nomatch;
  for (int i = 0; i < n; i++) {
    if (a[i] == b[i]) {
      match.push_back(i);
      if (a[i] == 'a')
        ans.push_back('b');
      else
        ans.push_back('a');
    } else {
      nomatch.push_back(i);
      if (a[i] != 'a' && b[i] != 'a')
        ans.push_back('a');
      else if (a[i] != 'b' && b[i] != 'b')
        ans.push_back('b');
      else if (a[i] != 'c' && b[i] != 'c')
        ans.push_back('c');
      else
        assert(false);
    }
  }
  t = n - t;
  int k = 0;
  while (t) {
    if (k == (int)match.size()) break;
    ans[match[k]] = a[match[k]];
    k++;
    t--;
  }
  k = 0;
  while (t) {
    if (k + 1 < (int)nomatch.size()) {
      ans[nomatch[k]] = a[nomatch[k]];
      ans[nomatch[k + 1]] = b[nomatch[k + 1]];
      k += 2;
      t--;
    } else
      break;
  }
  if (t)
    cout << -1;
  else
    cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}