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;
const int N = 100100;
char a[N], b[N], c[N];
int n, m, i, j, k;
int main() {
  scanf("%d%d", &n, &m);
  scanf("%s", a + 1);
  scanf("%s", b + 1);
  for (i = 1; i <= n; i++) k += a[i] != b[i];
  if (k > (m << 1)) {
    printf("-1\n");
    return 0;
  }
  m <<= 1;
  for (i = 1; i <= n; i++) {
    if (a[i] != b[i]) {
      if (k < m) {
        for (j = 'a'; j <= 'z'; j++)
          if (j != a[i] && j != b[i]) {
            c[i] = j;
            m -= 2;
            k--;
            break;
          }
      } else {
        if (m & 1)
          c[i] = a[i];
        else
          c[i] = b[i];
        m--;
        k--;
      }
    }
  }
  for (i = 1; i <= n; i++) {
    if (a[i] == b[i]) {
      if (m) {
        if (a[i] == 'a')
          c[i] = 'b';
        else
          c[i] = 'a';
        m -= 2;
      } else
        c[i] = a[i];
    }
  }
  printf("%s\n", c + 1);
  return 0;
}