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 str1[100010], str2[100010];
int n, t, same = 0;
char get_diff_char(char a, char b) {
  if (a != 'a' && b != 'a')
    return 'a';
  else if (a != 'b' && b != 'b')
    return 'b';
  else
    return 'c';
}
int main(void) {
  bool flag = true;
  scanf("%d %d", &n, &t);
  scanf("%s", str1);
  scanf("%s", str2);
  for (int i = 0; i < n; ++i)
    if (str1[i] == str2[i]) same++;
  if (t > n)
    flag = false;
  else {
    if (n - t > same + (n - same) / 2) flag = false;
  }
  if (flag) {
    int f, tmp;
    if (n - t > same) {
      f = n - t - same;
      tmp = 2;
      for (int i = 0; i < n; ++i)
        if (str1[i] == str2[i])
          printf("%c", str1[i]);
        else {
          if (f > 0) {
            if (tmp == 2)
              printf("%c", str1[i]);
            else
              printf("%c", str2[i]);
            tmp--;
            if (tmp == 0) {
              tmp = 2;
              f--;
            }
          } else {
            printf("%c", get_diff_char(str1[i], str2[i]));
          }
        }
    } else {
      f = n - t;
      for (int i = 0; i < n; ++i)
        if (str1[i] != str2[i])
          printf("%c", get_diff_char(str1[i], str2[i]));
        else {
          if (f > 0) {
            printf("%c", str1[i]);
            f--;
          } else {
            printf("%c", get_diff_char(str1[i], str2[i]));
          }
        }
    }
  } else {
    cout << -1 << endl;
  }
  return 0;
}