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 Answer[100100];
char Other(char c1, char c2);
int main() {
  memset(Answer, -1, sizeof(Answer));
  int n, t;
  cin >> n >> t;
  int Def = 0;
  string s1;
  cin >> s1;
  string s2;
  cin >> s2;
  for (int i = 0; i < n; i++) Def += (s1[i] != s2[i]);
  if (Def > 2 * t)
    cout << "-1";
  else {
    int T1 = t;
    for (int i = 0; i < n && T1; i++)
      if (s1[i] != s2[i]) {
        Answer[i] = s2[i];
        T1--;
      }
    int T2 = t;
    for (int i = n - 1; i >= 0 && T2; i--)
      if (s1[i] != s2[i]) {
        if (Answer[i] == -1)
          Answer[i] = s1[i];
        else
          Answer[i] = Other(s1[i], s2[i]);
        T2--;
      }
    for (int i = 0; i < n; i++)
      if (s1[i] == s2[i]) {
        if (T1)
          Answer[i] = Other(s1[i], s2[i]), T1--;
        else
          Answer[i] = s1[i];
      }
    for (int i = 0; i < n; i++) cout << Answer[i];
  }
}
char Other(char c1, char c2) {
  if (c1 != 'a' && c2 != 'a') return 'a';
  if (c1 != 'b' && c2 != 'b') return 'b';
  if (c1 != 'c' && c2 != 'c') return 'c';
}