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;
char letter(const char a, const char b) {
  char result = 'a';
  while (result == a || result == b) {
    result += 1;
  }
  return result;
}
using std::begin;
using std::end;
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(NULL);
  std::string s[2];
  uint64_t n, t;
  std::cin >> n >> t;
  s[0].reserve(n);
  s[1].reserve(n);
  std::cin >> s[0] >> s[1];
  std::vector<size_t> diff;
  diff.reserve(n);
  for (size_t i = 0; i < s[0].size(); ++i) {
    if (s[0][i] != s[1][i]) {
      diff.push_back(i);
    }
  }
  if (diff.size() > 2 * t) {
    std::cout << -1 << '\n';
    return 0;
  }
  string answer = s[0];
  if (diff.size() > t) {
    auto t2 = diff.size() - t;
    for (size_t i = t2; i < 2 * t2; ++i) {
      answer[diff[i]] = s[1][diff[i]];
    }
    for (size_t i = 2 * t2; i < diff.size(); ++i) {
      answer[diff[i]] = letter(s[0][diff[i]], s[1][diff[i]]);
    }
  } else {
    auto it = begin(diff);
    for (size_t i = 0; t > diff.size(); ++i) {
      if (it == end(diff) || i != *it) {
        answer[i] = letter(s[0][i], s[1][i]);
        t -= 1;
      }
      if (it != end(diff) && i >= *it) {
        ++it;
      }
    }
    for (size_t i = 0; i < diff.size(); ++i) {
      answer[diff[i]] = letter(s[0][diff[i]], s[1][diff[i]]);
    }
  }
  std::cout << answer << '\n';
}