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 n, t;
string s[3];
char dif(char a, char b) {
  if (a != 'a' and b != 'a') return 'a';
  if (a != 'b' and b != 'b') return 'b';
  return 'c';
}
int main() {
  cin >> n >> t >> s[0] >> s[1];
  int x = 0;
  int p = 0;
  for (int i = 0; i < n; ++i)
    if (s[0][i] == s[1][i]) p++;
  for (x = (n - p) % 2; x < n - p + 1; x += 2) {
    if (t == (x + ((n - p - x) / 2))) break;
    if (t < (x + ((n - p - x) / 2))) return cout << -1, 0;
  }
  if (x > (n - p)) x -= 2;
  int help = 0;
  int i;
  for (i = 0; (i < n) and (help < x); ++i) {
    if (s[0][i] == s[1][i]) {
      s[2] += s[0][i];
      continue;
    }
    s[2] += dif(s[0][i], s[1][i]);
    help++;
  }
  int flag = 1;
  for (; i < n; ++i) {
    if (s[0][i] == s[1][i]) {
      s[2] += s[0][i];
      continue;
    }
    s[2] += s[flag][i];
    flag = 1 - flag;
  }
  t -= (x + ((n - p - x) / 2));
  for (int j = 0; (j < n) and (t); ++j)
    if (s[0][j] == s[1][j]) {
      s[2][j] = dif(s[0][j], s[1][j]);
      t--;
    }
  cout << s[2];
}