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 MAXN = (int)2e5 + 47;
string s1, s2;
string ans;
char another(char x, char y) {
  for (char i = 'a'; i <= 'z'; i++) {
    if (x != i && y != i) return i;
  }
}
int main() {
  int n, t;
  cin >> n >> t;
  cin >> s1 >> s2;
  int good = 0, bad = 0;
  n = (int)s1.size();
  for (int i = 0; i < n; i++) {
    if (s1[i] != s2[i]) bad++;
  }
  int mint = bad % 2 + bad / 2;
  if (mint > t) {
    cout << -1;
    return 0;
  }
  int t1 = 0, t2 = 0;
  ans.resize(n);
  for (int i = 0; i < n; i++) {
    if (s1[i] == s2[i]) {
      ans[i] = s1[i];
      continue;
    }
    if (t1 <= t2) {
      ans[i] = s2[i];
      t1++;
    } else {
      ans[i] = s1[i];
      t2++;
    }
  }
  for (int i = 0; i < n; i++) {
    if (t1 != t2 && ans[i] == s2[i] && s1[i] != s2[i]) {
      ans[i] = another(s1[i], s2[i]);
      t2++;
      break;
    }
  }
  vector<int> b1, b2;
  good = 0;
  for (int i = 0; i < n; i++) {
    if (s1[i] != s2[i]) {
      if (ans[i] == s1[i])
        b1.push_back(i);
      else if (ans[i] == s2[i])
        b2.push_back(i);
    } else if (t2 < t && s1[i] == s2[i] && ans[i] == s1[i]) {
      ans[i] = another(s1[i], s2[i]);
      t1++;
      t2++;
    }
  }
  int sz1 = b1.size(), sz2 = b2.size();
  int ind1 = 0, ind2 = 0;
  while (t2 < t && ind1 < sz1 && ind2 < sz2) {
    ans[b1[ind1]] = another(s1[b1[ind1]], s2[b1[ind1]]);
    ans[b2[ind2]] = another(s1[b2[ind2]], s2[b2[ind2]]);
    ind1++;
    ind2++;
    t1++;
    t2++;
  }
  cout << ans;
  return 0;
}