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 dif(char c1) {
  if (c1 == 'a') return 'b';
  return 'a';
}
char dif2(char c1, char c2) {
  if (c1 != 'a' && c2 != 'a') return 'a';
  if (c1 != 'b' && c2 != 'b') return 'b';
  return 'c';
}
int main() {
  int n, t;
  cin >> n >> t;
  string s1, s2;
  cin >> s1 >> s2;
  vector<int> com;
  vector<int> nocom;
  for (long long i = 0; i < (n); i++)
    if (s1[i] == s2[i])
      com.push_back(i);
    else
      nocom.push_back(i);
  int comsz = com.size();
  int nocomsz = nocom.size();
  if (!(2 * t >= nocomsz)) {
    cout << -1 << endl;
    return 0;
  }
  string s3 = s1;
  if (nocomsz & 1) {
    int ind = nocom[nocomsz - 1];
    s3[ind] = dif2(s1[ind], s2[ind]);
    t--;
  }
  for (int i = 0; (i + 1 < nocomsz) && t > 0; i += 2) {
    int ind1 = nocom[i];
    s3[ind1] = s2[ind1];
    int ind2 = nocom[i + 1];
    s3[ind2] = s1[ind2];
    t--;
  }
  for (int i = 0; i < comsz && t > 0; i++) {
    int ind = com[i];
    s3[ind] = dif(s1[ind]);
    t--;
  }
  for (int i = 0; (i + 1 < nocomsz) && t > 0; i += 2) {
    int ind1 = nocom[i];
    int ind2 = nocom[i + 1];
    s3[ind1] = dif2(s1[ind1], s2[ind1]);
    s3[ind2] = dif2(s1[ind2], s2[ind2]);
    t--;
  }
  cout << s3 << endl;
}