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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, t;
  cin >> n >> t;
  t *= 2;
  string s1, s2, s3;
  cin >> s1 >> s2;
  s3.reserve(s1.size());
  bool diff = 0;
  for (auto i = 0; i != s1.size(); i++) {
    if (s1[i] != s2[i]) {
      t--;
    }
  }
  for (auto i = 0; i < s1.size(); i++) {
    if (s1[i] == s2[i]) {
      if (t >= 2) {
        auto c = 'a';
        if (s1[i] == c) {
          c = 'b';
          if (s2[i] == c) {
            c = 'c';
          }
        }
        if (s2[i] == c) {
          c = 'b';
          if (s1[i] == c) {
            c = 'c';
          }
        }
        s3.push_back(c);
        t -= 2;
      } else {
        s3.push_back(s1[i]);
      }
    } else {
      if (t > 0) {
        auto c = 'a';
        if (s1[i] == c) {
          c = 'b';
          if (s2[i] == c) {
            c = 'c';
          }
        }
        if (s2[i] == c) {
          c = 'b';
          if (s1[i] == c) {
            c = 'c';
          }
        }
        s3.push_back(c);
        t--;
      } else {
        diff = !diff;
        if (diff % 2 == 1) {
          s3.push_back(s1[i]);
        } else {
          s3.push_back(s2[i]);
        }
      }
    }
  }
  if (t != 0) {
    cout << -1;
  } else {
    cout << s3;
  }
  return 0;
}