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 getDiff(char a, char b) {
  char res = 'a';
  while (res == a || res == b) res++;
  return res;
}
int main() {
  ios::sync_with_stdio(0);
  int n, t;
  string s1, s2;
  cin >> n >> t >> s1 >> s2;
  int x = 0, y = 0;
  for (int i = 0; i < n; ++i) {
    if (s1[i] != s2[i])
      x++;
    else
      y++;
  }
  int a = -1, b = -1, c = -1, d = -1, e;
  for (e = 0; e <= y; ++e) {
    d = y - e;
    a = e + x - t;
    b = e + x - t;
    c = x - a - b;
    if (a < 0 || b < 0 || c < 0) {
      a = -1;
      continue;
    }
    break;
  }
  if (a == -1) {
    cout << "-1\n";
    return 0;
  }
  for (int i = 0; i < n; ++i)
    if (s1[i] != s2[i]) {
      if (a > 0) {
        cout << s2[i];
        a--;
      } else if (b > 0) {
        cout << s1[i];
        b--;
      } else if (c > 0) {
        cout << getDiff(s1[i], s2[i]);
        c--;
      } else
        while (1)
          ;
    } else {
      if (e > 0) {
        cout << getDiff(s1[i], s2[i]);
        e--;
      } else if (d > 0) {
        cout << s1[i];
        d--;
      } else
        exit(-1);
    }
  return 0;
}