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 getInt(char c) { return (int)(c - 'a'); }
char getChar(int i) { return (char)(i + 'a'); }
int getValue(string a, string b, int m) {
  int i;
  int ans = 0;
  for (i = 0; i < a.size(); i++)
    if (a[i] != b[i]) {
      ans++;
      if (ans > m) return -1;
    }
  return 1;
}
int main() {
  int n, d;
  cin >> n >> d;
  string s, t;
  cin >> s >> t;
  int r = n - d, e = n - d, i, j;
  vector<int> idx;
  int a[200005];
  for (i = 0; i < n; i++)
    if (s[i] == t[i]) idx.push_back(i);
  for (i = 0; i < idx.size(); i++) {
    if (r == 0 && e == 0) break;
    a[idx[i]] = getInt(s[idx[i]]) + 1;
    r--;
    e--;
  }
  bool f = true;
  for (i = 0; i < n; i++) {
    if (r == 0 && e == 0) break;
    if (s[i] != t[i] && a[i] == 0) {
      if (f) {
        a[i] = getInt(s[i]) + 1;
        r--;
        f = false;
      } else {
        a[i] = getInt(t[i]) + 1;
        e--;
        f = true;
      }
    }
  }
  if (r != 0 || e != 0) {
    cout << -1;
    return 0;
  }
  for (i = 0; i < n; i++)
    if (a[i] == 0)
      for (j = 0; j < 26; j++)
        if (getChar(j) != s[i] && getChar(j) != t[i]) {
          a[i] = j + 1;
          break;
        }
  string ans = "";
  for (i = 0; i < n; i++) {
    if (a[i] == 0) {
      cout << -1;
      return 0;
    }
    ans += getChar(a[i] - 1);
  }
  if (getValue(ans, s, d) == 1 && getValue(ans, t, d) == 1)
    cout << ans;
  else
    cout << -1;
  return 0;
}