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;
long long int pow_mod(long long int a, long long int b) {
  long long int res = 1;
  while (b != 0) {
    if (b & 1) {
      res = (res * a) % 1000000007;
    }
    a = (a * a) % 1000000007;
    b /= 2;
  }
  return res;
}
void solve() {
  long long int n, t;
  cin >> n >> t;
  string s1, s2;
  cin >> s1 >> s2;
  string ans;
  ans = s1;
  long long int dif = 0;
  for (long long int i = 0; i < n; i++) {
    if (s1[i] != s2[i]) dif++;
  }
  long long int toggle = -1;
  long long int dif_dif = -1;
  long long int same_dif = -1;
  long long int same_rem = -1;
  for (long long int i = 0; i <= dif; i += 2) {
    long long int pairs = i / 2;
    if (pairs > t) break;
    long long int rem = t - pairs;
    if (rem >= dif - i) {
      long long int d_rem = rem - dif + i;
      if (d_rem <= n - dif) {
        toggle = i;
        dif_dif = dif - i;
        same_dif = d_rem;
        same_rem = n - dif - same_dif;
        break;
      }
    }
  }
  if (toggle == -1)
    ans = "-1";
  else {
    long long int cnt = 0;
    long long int x = 0;
    for (long long int i = 0; i < n; i++) {
      if (toggle) {
        if (s1[i] != s2[i]) {
          if (x == 1) ans[i] = s2[i];
          x ^= 1;
          toggle--;
        }
      } else {
        if (s1[i] != s2[i]) {
          if (s1[i] != 'a' && s2[i] != 'a')
            ans[i] = 'a';
          else if (s1[i] != 'b' && s2[i] != 'b')
            ans[i] = 'b';
          else
            ans[i] = 'c';
        }
      }
    }
    for (long long int i = 0; i < n; i++) {
      if (s1[i] == s2[i]) {
        if (same_dif) {
          same_dif--;
          if (s1[i] == 'a')
            ans[i] = 'b';
          else
            ans[i] = 'a';
        }
      }
    }
  }
  cout << ans << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int t;
  t = 1;
  while (t--) solve();
  return 0;
}