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 dp[105];
int main() {
  int n, k;
  string l = "abc";
  cin >> n >> k;
  k = n - k;
  string a, b;
  cin >> a >> b;
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    if (a[i] == b[i]) cnt++;
  }
  int resto = n - cnt;
  resto /= 2;
  if (cnt + resto < k) {
    cout << -1 << "\n";
    return 0;
  }
  int ini = min(k, cnt);
  int fini = k - ini;
  string p = a;
  fini *= 2;
  for (int i = 0; i < n; i++) {
    if (a[i] == b[i] && ini > 0) {
      ini--;
    } else if (a[i] == b[i]) {
      for (int j = 0; j < 3; j++) {
        if (a[i] != l[j]) {
          p[i] = l[j];
          break;
        }
      }
    } else if (fini > 0) {
      if (fini % 2 == 0)
        p[i] = a[i];
      else if (fini % 2 == 1)
        p[i] = b[i];
      fini--;
    } else {
      for (int j = 0; j < 3; j++) {
        if (a[i] != l[j] && b[i] != l[j]) {
          p[i] = l[j];
          break;
        }
      }
    }
  }
  cout << p << "\n";
  return 0;
}