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;
string s1, s2;
bool match[100005];
int main() {
  int n, t, i, j;
  string ans;
  cin >> n >> t;
  cin >> s1 >> s2;
  int m = 0;
  for (i = 0; i < n; i++) {
    if (s1[i] == s2[i]) {
      match[i] = true;
      m++;
    }
  }
  if (m >= n - t) {
    ans = "";
    for (i = 0, j = 0; i < n; i++) {
      if (j < n - t && match[i]) {
        ans += s1[i];
        j++;
      } else {
        char ch = 'a';
        while (ch == s1[i] || ch == s2[i]) {
          ch++;
          if (ch == 123) ch = 'a';
        }
        ans += ch;
      }
    }
    ans == "\n";
  } else if (2 * (n - t - m) <= n - m) {
    ans = "";
    int cnt1 = n - t - m;
    int cnt2 = cnt1;
    for (i = 0; i < n; i++) {
      if (match[i])
        ans += s1[i];
      else if (cnt1) {
        ans += s1[i];
        cnt1--;
      } else if (cnt2) {
        ans += s2[i];
        cnt2--;
      } else {
        char ch = 'a';
        while (ch == s1[i] || ch == s2[i]) {
          ch++;
          if (ch == 123) ch = 'a';
        }
        ans += ch;
      }
    }
    ans == "\n";
  } else
    ans = "-1\n";
  cout << ans;
  return 0;
}