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;
void solve(long long tz) {
  int n, m;
  cin >> n >> m;
  int req = n - m;
  string s;
  cin >> s;
  string t;
  cin >> t;
  int same = 0;
  for (int i = 0; i < n; i++) {
    if (s[i] == t[i]) {
      same++;
    }
  }
  if (same == req) {
    string res;
    for (int i = 0; i < n; i++) {
      if (s[i] == t[i]) {
        res += s[i];
      } else {
        if (s[i] != 'z' && t[i] != 'z') {
          res += 'z';
        } else if (s[i] != 'a' && t[i] != 'a') {
          res += 'a';
        } else if (s[i] != 'c' && t[i] != 'c') {
          res += 'c';
        }
      }
    }
    cout << res << endl;
  } else if (same > req) {
    string res;
    int cnt = 0;
    for (int i = 0; i < n; i++) {
      if (s[i] == t[i] && cnt < req) {
        res += s[i];
        cnt++;
      } else if (s[i] == t[i] && cnt == req) {
        if (s[i] == 'z') {
          res += 'y';
        } else {
          res += 'z';
        }
      } else {
        if (s[i] != 'z' && t[i] != 'z') {
          res += 'z';
        } else if (s[i] != 'a' && t[i] != 'a') {
          res += 'a';
        } else if (s[i] != 'c' && t[i] != 'c') {
          res += 'c';
        }
      }
    }
    cout << res << endl;
  } else if (same < req) {
    int need = req - same;
    int count = 0;
    for (int i = 0; i < n; i++) {
      if (s[i] != t[i]) {
        count++;
      }
    }
    int num = 0;
    if (count < need * 2) {
      cout << "-1" << endl;
    } else {
      int index1 = 0;
      int index2 = 0;
      int cnt1 = 0;
      vector<char> arr(n);
      for (int i = 0; i < n; i++) {
        if (s[i] != t[i] && num < need) {
          if (cnt1 == 0) {
            index1 = i;
            cnt1++;
          } else if (cnt1 == 1) {
            arr[index1] = s[index1];
            arr[i] = t[i];
            cnt1 = 0;
            num++;
          }
        } else if (s[i] != t[i] && num == need) {
          if (s[i] != 'z' && t[i] != 'z') {
            arr[i] = 'z';
          } else if (s[i] != 'a' && t[i] != 'a') {
            arr[i] = 'a';
          } else if (s[i] != 'c' && t[i] != 'c') {
            arr[i] = 'c';
          }
        } else {
          arr[i] = s[i];
        }
      }
      string res;
      for (int i = 0; i < n; i++) {
        res += arr[i];
      }
      cout << res << endl;
    }
  }
}
int main() {
  long long t;
  t = 1;
  long long z = 0;
  while (t--) {
    z++;
    solve(z);
  }
}