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;
bool used[100010];
int main() {
  int n, t;
  memset(used, false, sizeof(used));
  cin >> n >> t;
  string s1, s2, s3;
  cin >> s1 >> s2;
  s3 = s1;
  int match, mis;
  match = mis = 0;
  for (int i = 0; i < n; i++)
    if (s1[i] == s2[i])
      match++;
    else
      mis++;
  t = n - t;
  if (match + mis / 2 < t) {
    cout << -1 << endl;
    return 0;
  }
  int cnt = 0;
  int f1, f2;
  f1 = f2 = 0;
  for (int i = 0; i < n; i++) {
    if (s1[i] == s2[i] and cnt < t) {
      s3[i] = s1[i];
      used[i] = true;
      cnt++;
    }
  }
  for (int i = 0; i < n; i++) {
    if (s1[i] != s2[i] and f1 + cnt < t) {
      s3[i] = s1[i];
      f1++;
    } else if (s1[i] != s2[i] and f2 + cnt < t) {
      s3[i] = s2[i];
      f2++;
    } else if (cnt + f1 >= t and cnt + f2 >= t and used[i] == false) {
      s3[i] = 'a';
      if (s3[i] == s1[i]) s3[i]++;
      if (s3[i] == s2[i]) s3[i]++;
      if (s3[i] == s1[i]) s3[i]++;
    }
  }
  cout << s3 << endl;
  return 0;
}