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;
multiset<int> mst;
set<int> st;
set<int>::iterator it;
vector<long long int> g[1001000];
map<long long int, long long int> mp[1001000], m1[1001000], m2[1001000];
int main() {
  long long int ans = 0;
  int n, t;
  cin >> n >> t;
  string s1, s2, s3;
  cin >> s1 >> s2;
  int ct = 0;
  char a[n + 2];
  for (int i = 0; i < s1.length(); ++i) {
    a[i] = '1';
    if (s1[i] == s2[i]) ct++;
  }
  int d1 = 0, d2 = 0;
  a[n] = '\0';
  for (int i = 0; i < s1.length(); ++i) {
    if (s1[i] == s2[i]) a[i] = s1[i];
  }
  int l = s1.length();
  int ctc = ct;
  if (ct > n - t) {
    for (int i = 0; i < l; ++i) {
      if (s1[i] == s2[i] && s1[i] != 'a')
        a[i] = 'a', ctc--;
      else if (s1[i] == s2[i] && s1[i] == 'a')
        a[i] = 'b', ctc--;
      if (ctc == n - t) break;
    }
    for (int i = 0; i < l; ++i) {
      if (s1[i] != s2[i] && s1[i] != 'a' && s2[i] != 'a')
        a[i] = 'a';
      else if (s1[i] != s2[i] && s1[i] != 'a' && s2[i] == 'a') {
        if (s1[i] != 'b')
          a[i] = 'b';
        else
          a[i] = 'c';
      } else if (s1[i] != s2[i] && s1[i] == 'a' && s2[i] != 'a') {
        if (s2[i] != 'b')
          a[i] = 'b';
        else
          a[i] = 'c';
      }
    }
  }
  if (ct <= n - t) {
    if (2 * (n - t - ct) + ct > n) {
      cout << -1 << endl;
      return 0;
    }
    for (int i = 0; i < l; ++i) {
      if (s1[i] != s2[i]) {
        if (d1 == n - t - ct && d2 == n - t - ct) {
          if (s1[i] != 'a' && s2[i] != 'a')
            a[i] = 'a';
          else if (s1[i] != 'a' && s2[i] == 'a') {
            if (s1[i] != 'b')
              a[i] = 'b';
            else
              a[i] = 'c';
          } else if (s1[i] == 'a' && s2[i] != 'a') {
            if (s2[i] != 'b')
              a[i] = 'b';
            else
              a[i] = 'c';
          }
          continue;
        }
        if (d1 != n - t - ct)
          a[i] = s1[i], d1++;
        else if (d2 != n - t - ct)
          a[i] = s2[i], d2++;
      }
    }
  }
  cout << a;
}