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;
int main(void) {
  int n, t, same, x, y;
  scanf("%d%d ", &n, &t);
  char *str1 = (char *)malloc((n + 1) * sizeof(char));
  char *str2 = (char *)malloc((n + 1) * sizeof(char));
  same = 0;
  for (int i = 0; i < n; ++i) {
    str1[i] = getchar();
  }
  getchar();
  for (int i = 0; i < n; ++i) {
    str2[i] = getchar();
    if (str2[i] == str1[i]) ++same;
  }
  if ((n - t - same) * 2 > n - same) {
    printf("-1");
    return 0;
  }
  x = 2 * (n - t - same);
  if (x < 0) x = 0;
  y = n - t;
  for (int i = 0; i < n; ++i) {
    if (str1[i] != str2[i]) {
      if (x > 0) {
        if (x % 2)
          printf("%c", str1[i]);
        else
          printf("%c", str2[i]);
        --x;
      } else {
        if (str1[i] != 'a' && str2[i] != 'a') {
          printf("a");
        } else if (str1[i] != 'b' && str2[i] != 'b') {
          printf("b");
        } else
          printf("c");
      }
    } else {
      if (y > 0) {
        printf("%c", str1[i]);
        --y;
      } else {
        if (str1[i] != 'a')
          printf("a");
        else
          printf("b");
      }
    }
  }
  return 0;
}