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, d, t, i;
  string s1, s2, s3;
  cin >> n >> t >> s1 >> s2;
  s3 = s1;
  d = 0;
  for (i = 0; i < n; i++)
    if (s1[i] != s2[i]) d++;
  int r = t - d;
  if (d <= t) {
    for (i = 0; i < n; i++) {
      if (s1[i] != s2[i]) {
        if (s1[i] != 'a' && s2[i] != 'a')
          s3[i] = 'a';
        else if (s1[i] != 'b' && s2[i] != 'b')
          s3[i] = 'b';
        else if (s1[i] != 'c' && s2[i] != 'c')
          s3[i] = 'c';
      } else if (s1[i] == s2[i] && r > 0) {
        if (s1[i] != 'a')
          s3[i] = 'a';
        else if (s1[i] != 'b')
          s3[i] = 'b';
        else if (s1[i] != 'c')
          s3[i] = 'c';
        r--;
      }
    }
    cout << s3;
  } else if (d / 2 + d % 2 <= t) {
    r = -r;
    for (i = 0; i < n && t > 0 && r > 0; i++) {
      if (s1[i] != s2[i]) {
        s3[i] = s2[i];
        t--, r--;
      }
    }
    for (; i < n && t > 0 && r == 0; i++) {
      if (s1[i] != s2[i]) {
        if (s1[i] != 'a' && s2[i] != 'a')
          s3[i] = 'a';
        else if (s1[i] != 'b' && s2[i] != 'b')
          s3[i] = 'b';
        else if (s1[i] != 'c' && s2[i] != 'c')
          s3[i] = 'c';
        t--;
      }
    }
    cout << s3;
  } else
    cout << -1;
  return 0;
}