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() {
  int n, t;
  cin >> n >> t;
  string a, b;
  cin >> a >> b;
  int sim = 0;
  for (int i = 0; i < n; i++)
    if (a[i] == b[i]) sim++;
  int x = n - t;
  if (x > sim && n - sim >= (x - sim) * 2) {
    string second = a;
    int y1 = x - sim, y2 = y1;
    for (int i = 0; i < n; i++) {
      if (a[i] != b[i]) {
        if (y1)
          y1--;
        else if (y2) {
          y2--;
          second[i] = b[i];
        } else {
          for (int j = 0; j < 26; j++) {
            if (a[i] != j + 'a' && b[i] != j + 'a') {
              second[i] = j + 'a';
              break;
            }
          }
        }
      }
    }
    cout << second << "\n";
  } else if (x <= sim) {
    string second = a;
    for (int i = 0; i < n; i++) {
      if (a[i] == b[i]) {
        if (x) {
          x--;
        } else {
          for (int j = 0; j < 26; j++) {
            if (a[i] != j + 'a' && b[i] != j + 'a') {
              second[i] = j + 'a';
              break;
            }
          }
        }
      } else {
        for (int j = 0; j < 26; j++) {
          if (a[i] != j + 'a' && b[i] != j + 'a') {
            second[i] = j + 'a';
            break;
          }
        }
      }
    }
    cout << second << "\n";
  } else {
    cout << -1 << '\n';
  }
}