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 ara[26];
int main() {
  int n, t;
  string s1, s2;
  cin >> n >> t >> s1 >> s2;
  string ans = "";
  bool noAns = false;
  int match = n - t, same = 0;
  for (int i = 0; i < n; i++) {
    if (s1[i] == s2[i]) same++;
  }
  int NoTchange = same, change1 = 0, change2 = 0;
  int matchbosha = match;
  change1 = match - same;
  change2 = change1;
  if (same >= match) {
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i] and NoTchange > 0 and match > 0)
        ans += s1[i], NoTchange--, match--;
      else {
        memset(ara, 0, sizeof(ara));
        ara[s1[i] - 'a'] = 1;
        ara[s2[i] - 'a'] = 1;
        if (s1[i] == s2[i] and s1[i] != 'a')
          ans += "a";
        else if (s1[i] == s2[i] and s1[i] == 'a')
          ans += "z";
        else if (ara[0] == 0)
          ans += "a";
        else if (ara[1] == 0)
          ans += "b";
        else if (ara[2] == 0)
          ans += "c";
      }
    }
  } else if (n < same + (change1 * 2)) {
    noAns = true;
  } else {
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i])
        ans += s1[i];
      else if (change1 > 0)
        ans += s1[i], change1--;
      else if (change2 > 0)
        ans += s2[i], change2--;
      else {
        memset(ara, 0, sizeof(ara));
        ara[s1[i] - 'a'] = 1;
        ara[s2[i] - 'a'] = 1;
        if (ara[0] == 0)
          ans += "a";
        else if (ara[1] == 0)
          ans += "b";
        else if (ara[2] == 0)
          ans += "c";
      }
    }
  }
  if (noAns or change1 > 0 or change2 > 0)
    cout << "-1";
  else
    cout << ans;
}