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 n1, i, l, j, k, n, m, ss1[100100], ss2[100030], ss3[100030];
char cc(char c1, char c2) {
  char c = 'c';
  if (c1 != 'a' && c2 != 'a')
    c = 'a';
  else if (c1 != 'b' && c2 != 'b')
    c = 'b';
  return c;
}
int main() {
  string s1, s2, s3 = "";
  cin >> l >> m;
  cin >> s1 >> s2;
  int match = 0;
  for (i = 0; i < l; i++) {
    if (s1.at(i) == s2.at(i)) match++;
  }
  bool tr = true;
  m = l - m;
  if (m <= match) {
    match = m;
    m = 0;
    j = 0;
  } else {
    for (i = 0; i <= match; i++) {
      j = m - i;
      k = l - i - 2 * j;
      if (k >= 0 && k + i >= match) {
        tr = true;
        break;
      } else
        tr = false;
    }
    if (k < 0) tr = false;
    match = i;
  }
  if (tr == false) {
    cout << -1 << endl;
    return 0;
  }
  int l1 = j, l2 = j;
  m = l - 2 * j - match;
  for (i = 0; i < l; i++) {
    if (s1.at(i) == s2.at(i)) {
      if (match) {
        match--;
        s3.insert(i, 1, s1.at(i));
      } else
        s3.insert(i, 1, cc(s1.at(i), s2.at(i)));
    } else if (l1) {
      l1--;
      s3.insert(i, 1, s1.at(i));
    } else if (l2) {
      l2--;
      s3.insert(i, 1, s2.at(i));
    } else {
      s3.insert(i, 1, cc(s1.at(i), s2.at(i)));
    }
  }
  cout << s3 << endl;
  return 0;
}