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 next_char(char c) {
  const int mod = 'z' - 'a' + 1;
  return 'a' + (c - 'a' + 1) % mod;
}
int main() {
  int n, t;
  scanf("%d %d", &n, &t);
  vector<char> s1(n + 1, ' '), s2(n + 1, ' '), s3(n + 1, ' ');
  scanf("%s", s1.data());
  scanf("%s", s2.data());
  int same = 0;
  for (int i = 0; i < n; ++i) {
    if (s1[i] == s2[i]) {
      ++same;
    }
  }
  int diff = n - same;
  if (t < (diff + 1) / 2) {
    printf("-1\n");
    return 0;
  }
  int t1, t2;
  t1 = t2 = n - t;
  int x = min(n - t, same);
  for (int i = 0; i < n; ++i) {
    if (s1[i] == s2[i] && t1 > 0 && t2 > 0) {
      s3[i] = s1[i];
      --t1;
      --t2;
      --x;
    } else {
      if (s1[i] != s2[i]) {
        if (t1 > x) {
          s3[i] = s1[i];
          --t1;
          continue;
        }
        if (t2 > x) {
          s3[i] = s2[i];
          --t2;
          continue;
        }
      }
      const int mod = 'z' - 'a' + 1;
      char next = next_char(s1[i]);
      if (next == s2[i]) next = next_char(s2[i]);
      s3[i] = next;
    }
  }
  s3[n] = '\0';
  printf("%s\n", s3.data());
}