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 = 1e5 + 1;
int n, t;
vector<int> v, u;
string s1, s2;
char s3[MAXN];
char dif(char a, char b) {
  if (a == 'a' or b == 'a') {
    if (a == 'b' or b == 'b')
      return 'c';
    else
      return 'b';
  } else
    return 'a';
}
int main() {
  cin >> n >> t >> s1 >> s2;
  for (int i = 0; i < n; i++)
    if (s1[i] == s2[i])
      v.push_back(i);
    else
      u.push_back(i);
  int m = u.size(), c = 0;
  if (t < (m + 1) / 2) {
    cout << -1;
    return 0;
  }
  for (auto i : v) s3[i] = s1[i];
  for (int i = 0; i < m; i++)
    if (i % 2)
      s3[u[i]] = s1[u[i]];
    else
      s3[u[i]] = s2[u[i]];
  if (m % 2) s3[u.back()] = dif(s1[u.back()], s2[u.back()]);
  c = (m + 1) / 2;
  for (int i = 0; i < v.size() and c < t; i++) {
    s3[v[i]] = dif(s1[v[i]], s2[v[i]]);
    c++;
  }
  for (int i = 0; i < m - (m % 2) and c < t; i += 2) {
    s3[u[i]] = dif(s1[u[i]], s2[u[i]]);
    s3[u[i + 1]] = dif(s1[u[i + 1]], s2[u[i + 1]]);
    c++;
  }
  if (c < t) {
    cout << -1;
    return 0;
  }
  for (int i = 0; i < n; i++) cout << s3[i];
}