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 inf = 1e9 + 100500;
const int maxn = 100500;
string s, t;
int p;
vector<int> a, b;
string r;
int n;
int main() {
  cin >> n >> p >> s >> t;
  r = string(s.length(), '.');
  for (int i = 0; i < (int)(s.length()); ++i) {
    if (s[i] == t[i])
      a.push_back(i);
    else
      b.push_back(i);
  }
  while (p && !b.empty() && ((int)b.size()) / 2 <= p - 1) {
    int i = b.back();
    b.pop_back();
    for (int c = (int)('a'); c <= (int)('z'); ++c)
      if (s[i] != c && t[i] != c) {
        r[i] = c;
        break;
      }
    --p;
  }
  if ((int)b.size() / 2 > p) {
    cout << -1 << endl;
    return 0;
  }
  if (b.size() % 2) {
    cout << -1 << endl;
    return 0;
  }
  for (int i = 0; i < (int)(b.size()); ++i) {
    if (i % 2)
      r[b[i]] = s[b[i]], --p;
    else
      r[b[i]] = t[b[i]];
  }
  for (int i = 0; i < (int)(a.size()); ++i) r[a[i]] = s[a[i]];
  for (int i = 0; i < (int)(p); ++i) r[a[i]] = 'a' + (s[a[i]] - 'a' + 1) % 26;
  cout << r << endl;
  return 0;
}