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() {
  long long n, t;
  string a, b;
  cin >> n >> t >> a >> b;
  t = n - t;
  vector<long long> v1, v2;
  for (int i = 0; i < n; i++)
    if (a[i] == b[i])
      v1.push_back(i);
    else
      v2.push_back(i);
  for (int i = 0; i <= v1.size() && i <= t; i++)
    if ((t - i) * 2 <= v2.size()) {
      vector<char> d(n);
      for (int j = 0; j < i; j++) d[v1[j]] = a[v1[j]];
      for (int j = i; j < v1.size(); j++)
        d[v1[j]] = (char)((a[v1[j]] - 'a' + 1) % 26 + 'a');
      for (int j = 0; j < t - i; j++) d[v2[j]] = a[v2[j]];
      for (int j = t - i; j < 2 * (t - i); j++) d[v2[j]] = b[v2[j]];
      for (int j = 2 * (t - i); j < v2.size(); j++) {
        char c = a[v2[j]];
        c = (char)((c - 'a' + 1) % 26 + 'a');
        if (c == b[v2[j]]) c = (char)((c - 'a' + 1) % 26 + 'a');
        d[v2[j]] = c;
      }
      for (auto x : d) cout << x;
      return 0;
    }
  cout << -1;
}