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 main() {
  int n, t, cnt = 0, cntt, cntt1, cntt2, c1 = 0, c2 = 0, prev = 1;
  string s1, s2, s3;
  cin >> n >> t >> s1 >> s2;
  for (int i = 0; i < n; i++) {
    if (s1[i] == s2[i]) cnt++;
    s3 += "0";
  }
  if (t >= (n - cnt)) {
    cntt = cnt;
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i] && (n - cntt) < t) {
        if (s1[i] + 1 <= 122)
          s3[i] = s1[i] + 1;
        else
          s3[i] = s1[i] - 1;
        cntt--;
      } else if (s1[i] != s2[i]) {
        if (s1[i] + 1 != s2[i] && s1[i] + 1 <= 122)
          s3[i] = s1[i] + 1;
        else if (s1[i] - 1 != s2[i] && s1[i] - 1 >= 97)
          s3[i] = s1[i] - 1;
        else if (s2[i] + 1 != s1[i] && s2[i] + 1 <= 122)
          s3[i] = s2[i] + 1;
        else
          s3[i] = s2[i] - 1;
      } else
        s3[i] = s2[i];
    }
  } else {
    cntt1 = (cntt2 = cnt);
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i] && prev == 1 && (n - cntt2) > t) {
        s3[i] = s2[i];
        prev = 2;
        cntt2++;
      } else if (s1[i] != s2[i] && prev == 2 && (n - cntt1) > t) {
        s3[i] = s1[i];
        prev = 1;
        cntt1++;
      } else if (s1[i] == s2[i]) {
        s3[i] = s2[i];
      } else {
        if (s1[i] + 1 != s2[i] && s1[i] + 1 <= 122)
          s3[i] = s1[i] + 1;
        else if (s1[i] - 1 != s2[i] && s1[i] - 1 >= 97)
          s3[i] = s1[i] - 1;
        else if (s2[i] + 1 != s1[i] && s2[i] + 1 <= 122)
          s3[i] = s2[i] + 1;
        else
          s3[i] = s2[i] - 1;
      }
    }
  }
  for (int i = 0; i < n; i++) {
    if (s3[i] != s1[i]) c1++;
    if (s3[i] != s2[i]) c2++;
    if (s3[i] == '0') {
      cout << "-1" << endl;
      return 0;
    }
  }
  if (c1 != t || c2 != t) {
    cout << "-1" << endl;
    return 0;
  }
  cout << s3 << endl;
  return 0;
}