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;
using LL = long long;
using ULL = unsigned long long;
using LD = long double;
using pii = pair<int, int>;
using pll = pair<LL, LL>;
using pld = pair<LD, LD>;
inline char get_diff(const char chr1, const char chr2) {
  if (chr1 != 'a' && chr2 != 'a') {
    return 'a';
  }
  if (chr1 != 'b' && chr2 != 'b') {
    return 'b';
  }
  return 'c';
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, t;
  cin >> n >> t;
  vector<string> strs(2);
  cin >> strs[0] >> strs[1];
  int nr_diff_poss = 0;
  string res(n, '?');
  vector<int> diff_poss, non_diff_poss;
  for (int i = 0; i < n; ++i) {
    if (strs[0][i] != strs[1][i]) {
      diff_poss.emplace_back(i);
      ++nr_diff_poss;
    } else {
      non_diff_poss.emplace_back(i);
      res[i] = strs[0][i];
    }
  }
  if (t <= (nr_diff_poss - 1) / 2) {
    if (strs[0] == strs[1] && t == 0) {
      cout << strs[0];
    } else {
      cout << "-1";
    }
    return 0;
  }
  bool str = 0;
  int nr_diff_chrs[2] = {0, 0};
  for (const int &pos : diff_poss) {
    res[pos] = strs[str][pos];
    str ^= 1;
    ++nr_diff_chrs[str];
  }
  if (nr_diff_chrs[0] != nr_diff_chrs[1]) {
    assert(!diff_poss.empty());
    assert(abs(nr_diff_chrs[0] - nr_diff_chrs[1]) <= 1);
    const int &pos = diff_poss.back();
    res[pos] = get_diff(strs[0][pos], strs[1][pos]);
    diff_poss.pop_back(), --nr_diff_poss;
    nr_diff_chrs[0] = nr_diff_chrs[1];
  }
  for (int i = 0; i < non_diff_poss.size() && nr_diff_chrs[0] < t; ++i) {
    const int &pos = non_diff_poss[i];
    res[pos] = get_diff(strs[0][pos], strs[0][pos]);
    ++nr_diff_chrs[0], ++nr_diff_chrs[1];
  }
  cerr << "string so far: '" << res << "'" << endl;
  for (int i = 0; nr_diff_chrs[0] < t || nr_diff_chrs[1] < t; ++i) {
    assert(i < nr_diff_poss);
    const int &pos = diff_poss[i];
    if (res[pos] == strs[0][pos]) {
      ++nr_diff_chrs[0];
    } else {
      ++nr_diff_chrs[1];
    }
    res[pos] = get_diff(strs[0][pos], strs[1][pos]);
  }
  cout << res;
}