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>
char a[110000], b[110000], c[110000];
int n, t, dif;
int main() {
  int t0, t1, t2, t3;
  scanf("%d%d", &n, &t);
  scanf("%s%s", a, b);
  dif = 0;
  for (int i = 0; i < n; i++)
    if (a[i] != b[i]) dif++;
  if (2 * t < dif || t > n)
    printf("-1\n");
  else {
    if (t >= dif) {
      t3 = dif;
      t1 = 0;
      t2 = 0;
      t0 = t - dif;
    } else {
      t3 = 2 * t - dif;
      t1 = dif - t;
      t2 = dif - t;
      t0 = 0;
    }
    for (int i = 0; i < n; i++)
      if (a[i] == b[i])
        if (t0) {
          c[i] = 'a';
          while (c[i] == a[i] || c[i] == b[i]) {
            c[i]++;
          }
          t0--;
        } else
          c[i] = a[i];
      else {
        if (t3) {
          c[i] = 'a';
          while (c[i] == a[i] || c[i] == b[i]) {
            c[i]++;
          }
          t3--;
          continue;
        }
        if (t1) {
          c[i] = a[i];
          t1--;
          continue;
        }
        if (t2) {
          c[i] = b[i];
          t2--;
          continue;
        }
        return -1;
      }
    c[n] = 0;
    printf("%s\n", c);
  }
}