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;
char newchar(char a, char b) {
  char cha;
  for (int i = 0; i < 26; ++i) {
    char ch = char('a' + i);
    if (ch != a && ch != b) {
      cha = ch;
      break;
    }
  }
  return cha;
}
char ans[100005];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n, t;
  string s1, s2;
  memset(ans, 0, sizeof(ans));
  cin >> n >> t >> s1 >> s2;
  int same_cnt = 0;
  for (int i = 0; i < n; ++i) {
    if (s1[i] == s2[i]) ++same_cnt;
  }
  t = n - t;
  if (n + same_cnt < 2 * (t)) {
    cout << -1;
    return 0;
  }
  int mn = min(t, same_cnt);
  int rem = (t - mn);
  for (int i = 0, j = 0; i < n && j < mn; ++i) {
    if (s1[i] == s2[i]) ans[i] = s1[i], ++j;
  }
  for (int i = 0, j = 0; i < n && j < rem; ++i) {
    if (s1[i] != s2[i] && !ans[i]) ans[i] = s1[i], ++j;
  }
  for (int i = 0, j = 0; i < n && j < rem; ++i) {
    if (s1[i] != s2[i] && !ans[i]) ans[i] = s2[i], ++j;
  }
  for (int i = 0; i < n; ++i) {
    if (!ans[i]) ans[i] = newchar(s1[i], s2[i]);
  }
  cout << ans;
}