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, a, b, c;
char s1[100001], s2[100001];
bool same[100001];
char dif(char d, char e) {
  for (int i = 0; i < 3; i++) {
    char f = 'a' + i;
    if (d != f && e != f) return f;
  }
}
int main() {
  cin >> n >> t;
  cin >> s1 >> s2;
  for (int i = 0; i < n; i++)
    if (s1[i] == s2[i]) a++, same[i] = 1;
  if (a + (n - a) / 2 < n - t) {
    cout << -1 << endl;
    return 0;
  }
  for (int i = 0; i < n; i++) {
    if (same[i])
      if (b + (c + 1) / 2 < n - t)
        b++, cout << s1[i];
      else
        cout << dif(s1[i], s2[i]);
    else if (b + c / 2 < n - t) {
      if (c % 2 == 0)
        if (n - a > 1)
          a++, c++, cout << s1[i];
        else
          cout << dif(s1[i], s2[i]);
      else
        a++, c++, cout << s2[i];
    } else
      cout << dif(s1[i], s2[i]);
  }
  cout << endl;
}