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;
char func(char a, char b) {
  for (char i = 'a'; i < 'z'; i++) {
    if (i != a && i != b) return i;
  }
}
int main() {
  char a[100007];
  char b[100007];
  char c[100007];
  int f1, f2, n, t, count = 0;
  cin >> n >> t;
  cin >> a >> b;
  for (int i = 0; i < n; i++) {
    if (a[i] != b[i]) count++;
  }
  if (count > 2 * t) {
    cout << "-1\n";
  } else if (count <= t) {
    f1 = t - count;
    f2 = count;
    for (int i = 0; i < n; i++) {
      if (a[i] == b[i]) {
        if (f1 > 0) {
          c[i] = func(a[i], b[i]);
          f1--;
        } else {
          c[i] = a[i];
        }
      }
      if (a[i] != b[i]) {
        c[i] = func(a[i], b[i]);
      }
    }
  } else {
    f1 = count - t;
    f2 = count - t;
    for (int i = 0; i < n; i++) {
      if (a[i] != b[i]) {
        if (f1 != 0) {
          c[i] = a[i];
          f1--;
        } else if (f2 != 0) {
          c[i] = b[i];
          f2--;
        } else {
          c[i] = func(a[i], b[i]);
        }
      } else
        c[i] = a[i];
    }
  }
  c[n] = '\0';
  cout << c << "\n";
}