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;
vector<int> Two_or_Zero;
vector<int> One_or_Two;
char Char_at[100666];
int Type[100666];
char Return_Diff_Chr(char c1, char c2) {
  for (char i = 'a'; i <= 'z'; ++i)
    if (i != c1 && i != c2) return i;
}
char plus_zero_one(char c1, char c2, int whos) { return (whos == 0 ? c1 : c2); }
void print_vec(vector<int> vec) {
  cout << '\n';
  cout << vec.size() << '\n';
  for (int i = 0; i < vec.size(); ++i) cout << vec[i] << " ";
  cout << '\n' << '\n';
}
int main() {
  int n, t, i;
  string s1, s2;
  string result;
  cin >> n >> t;
  cin.get();
  cin >> s1 >> s2;
  for (i = 0; i < n; ++i)
    if (s1[i] == s2[i])
      Two_or_Zero.push_back(i);
    else
      One_or_Two.push_back(i);
  int nr_Two_or_Zero = Two_or_Zero.size();
  int nr_One_or_Two = One_or_Two.size();
  bool itExists = false;
  int nr_Ones = 0;
  int nr_Two_Extra = 0;
  for (i = 0; i <= nr_One_or_Two; i += 2) {
    int t2 = t - i / 2;
    t2 -= nr_One_or_Two - i;
    if (t2 < 0) continue;
    if (t2 <= nr_Two_or_Zero) {
      itExists = true;
      nr_Ones = i;
      nr_Two_Extra = t2;
    }
  }
  if (itExists == false) {
    cout << -1 << '\n';
    return 0;
  }
  int pos;
  for (i = 0; i < nr_Ones; ++i) {
    pos = One_or_Two[i];
    Type[pos] = 1;
    Char_at[pos] = plus_zero_one(s1[pos], s2[pos], i % 2);
  }
  for (i = nr_Ones; i < nr_One_or_Two; ++i) {
    pos = One_or_Two[i];
    Type[pos] = 1;
    Char_at[pos] = Return_Diff_Chr(s1[pos], s2[pos]);
  }
  for (i = 0; i < nr_Two_Extra; ++i) {
    pos = Two_or_Zero[i];
    Type[pos] = 1;
    Char_at[pos] = Return_Diff_Chr(s1[pos], s2[pos]);
  }
  for (i = 0; i < n; ++i)
    if (Type[i] == 0)
      result += s1[i];
    else
      result += Char_at[i];
  cout << result << '\n';
  return 0;
}