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 file() {
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
}
void fast() {
  ios::sync_with_stdio(0);
  cin.tie(0);
}
int main() {
  int n, t;
  cin >> n >> t;
  int eq, diff;
  eq = diff = 0;
  string s, ss, ans;
  cin >> s >> ss;
  ans = s;
  vector<char> v;
  bool b = 0;
  for (char i = 'a'; i <= 'z'; i++) v.push_back(i);
  for (int i = 0; i < s.size(); i++)
    eq += (s[i] == ss[i]), diff += (s[i] != ss[i]);
  if (t * 2 < diff) return cout << -1 << endl, 0;
  for (int i = 0; i < s.size() && diff; i++) {
    if (s[i] != ss[i]) {
      if (t * 2 > diff) {
        int j = 0;
        while (v[j] == s[i] || v[j] == ss[i]) j++;
        ans[i] = v[j];
        t--, diff--;
      } else {
        if (!b)
          b = 1;
        else {
          ans[i] = ss[i];
          diff -= 2;
          t--;
          b = 0;
        }
      }
    }
  }
  if (t > eq) return cout << -1 << endl, 0;
  if (t) {
    for (int i = 0; i < s.size() && t; i++) {
      if (s[i] == ss[i]) {
        int j = 0;
        j += (v[j] == s[i]);
        ans[i] = v[j];
        t--;
      }
    }
  }
  cout << ans << endl;
  return 0;
}