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 main() {
  string s1, s2;
  int n;
  int diff = 0, t;
  cin >> n >> t;
  cin >> s1 >> s2;
  int count = 0, count2 = 0;
  for (int i = 0; i < s1.length(); i++) {
    if (s1[i] != s2[i]) {
      diff++;
    }
  }
  if (2 * t < diff) {
    cout << -1 << '\n';
    return 0;
  }
  if (diff >= t) {
    int ccnt = 0;
    count = diff - t;
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) {
        if (ccnt < count)
          cout << s1[i];
        else if (ccnt < 2 * count)
          cout << s2[i];
        else {
          if (s1[i] != 'a' and s2[i] != 'a')
            cout << 'a';
          else if (s1[i] != 'b' and s2[i] != 'b')
            cout << 'b';
          else if (s1[i] != 'c' and s2[i] != 'c')
            cout << 'c';
        }
        ccnt++;
      } else {
        cout << s1[i];
      }
    }
  } else {
    count = t - diff;
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) {
        if (s1[i] != 'a' and s2[i] != 'a')
          cout << 'a';
        else if (s1[i] != 'b' and s2[i] != 'b')
          cout << 'b';
        else if (s1[i] != 'c' and s2[i] != 'c')
          cout << 'c';
      } else {
        if (count) {
          if (s1[i] == 'a')
            cout << 'b';
          else
            cout << 'a';
          count--;
        } else
          cout << s1[i];
      }
    }
  }
  cout << endl;
  return 0;
}