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 double eps = 1e-5;
const double pi = acos(-1.0);
const int mod = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const int N = 1e5 + 7;
bool status[N];
char Generate(char a, char b) {
  char tmp;
  for (int i = 0; i < 26; i++) {
    tmp = 'a' + i;
    if (tmp != a && tmp != b) {
      return tmp;
    }
  }
}
int cout_dif(string a, string b, int len) {
  int res = 0;
  for (int i = 0; i < len; i++) {
    if (a[i] != b[i]) res++;
  }
  return res;
}
int main() {
  int n, t, dif = 0;
  string a, b, c;
  cin >> n >> t;
  cin >> a >> b;
  c = string(n, 'a');
  vector<int> pos;
  memset(status, 0, sizeof(status));
  for (int i = 0; i < n; i++) {
    if (a[i] != b[i])
      dif++;
    else
      status[i] = 1;
  }
  if (t == dif) {
    for (int i = 0; i < n; i++) {
      if (status[i]) {
        c[i] = a[i];
      } else
        c[i] = Generate(a[i], b[i]);
    }
  } else if (t > dif) {
    int cnt = 0;
    for (int i = 0; i < n; i++) {
      if (status[i]) {
        if (cnt < (t - dif)) {
          c[i] = Generate(a[i], b[i]);
          cnt++;
        } else
          c[i] = a[i];
      } else {
        c[i] = Generate(a[i], b[i]);
      }
    }
  } else {
    int cnt1 = 0, cnt2 = 0;
    for (int i = 0; i < n; i++) {
      if (status[i])
        c[i] = a[i];
      else {
        if (cnt1 < (dif - t)) {
          c[i] = a[i];
          cnt1++;
        } else if (cnt2 < (dif - t)) {
          c[i] = b[i];
          cnt2++;
        } else
          c[i] = Generate(a[i], b[i]);
      }
    }
  }
  if (cout_dif(a, c, n) == t && cout_dif(b, c, n) == t)
    cout << c << endl;
  else
    cout << "-1" << endl;
  return 0;
}