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 s3[200000];
string s1, s2;
int n, m, k, i, j, t, t1, t2, a, b, cur;
int main() {
  cin >> n >> t;
  cin >> s1 >> s2;
  t1 = t;
  t2 = t;
  for (i = 0; i < n; i++)
    if (s1[i] != s2[i]) cur++;
  a = cur / 2;
  for (i = 0; i < n; i++)
    if (s1[i] != s2[i]) {
      if (a) {
        a--;
        s3[i] = s1[i];
        t2--;
      } else {
        s3[i] = s2[i];
        t1--;
      }
    } else
      s3[i] = s1[i];
  for (i = 0; i < n; i++)
    if (s1[i] != s2[i]) {
      if (s3[i] == s1[i]) {
        if (t1 < 1) continue;
        t1--;
      } else {
        if (t2 < 1) continue;
        t2--;
      }
      for (j = 0; j <= 25; j++)
        if ((s1[i] - 'a') != j && (s2[i] - 'a') != j) {
          s3[i] = char(j + 'a');
          break;
        }
    }
  if (t1 < 0 || t2 < 0) {
    cout << -1;
    return 0;
  }
  for (i = 0; i < n; i++)
    if (s1[i] == s2[i] && t1 > 0 && t2 > 0) {
      if (s1[i] != 'z')
        s3[i] = 'z';
      else
        s3[i] = 'a';
      t1--;
      t2--;
    }
  if (t1 != 0 || t2 != 0) {
    cout << -1;
    return 0;
  }
  int cur1 = 0, cur2 = 0;
  for (i = 0; i < n; i++) {
    if (s1[i] != s3[i]) cur1++;
    if (s2[i] != s3[i]) cur2++;
  }
  if (cur1 != t || cur2 != t) {
    cout << -1;
    return 0;
  }
  for (i = 0; i < n; i++) cout << s3[i];
}