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;
const int N = 20000005;
int n, k, x, t, a, b, m;
string s1, s2;
vector<long long> v;
int main() {
  cin >> n >> t;
  cin >> s1 >> s2;
  int dif = 0;
  for (int i = 0; i < n; i++) {
    dif += (s1[i] != s2[i]);
  }
  if (dif > 2 * t) {
    cout << "-1";
  } else {
    int a = t, b = t;
    string res = "";
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) {
        if (dif * 2 <= a + b) {
          a--, b--;
          for (int j = 0; j < 3; j++) {
            if (s1[i] != ('a' + j) && s2[i] != ('a' + j)) {
              res += ('a' + j);
              break;
            }
          }
        } else {
          if (a > b) {
            res += s2[i];
            a--;
          } else {
            b--;
            res += s1[i];
          }
        }
        dif--;
      } else {
        res += s1[i];
      }
    }
    for (int i = 0; i < n && a + b; i++) {
      if (s1[i] == s2[i]) {
        a--, b--;
        res[i] = (s1[i] == 'a' ? 'b' : 'a');
      }
    }
    cout << res;
  }
  return 0;
}