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 INF = 0x3f3f3f3f;
const int MAXN = (int)2e5 + 5;
int t, n;
char a[MAXN], b[MAXN];
char s[MAXN];
int main() {
  cin >> n >> t;
  scanf(" %s %s", a, b);
  int cnt = 0;
  for (int i = 0; i < n; i++)
    if (a[i] == b[i]) cnt++;
  if (cnt + (n - cnt) / 2 < n - t) {
    printf("-1\n");
    return 0;
  }
  int cnt2 = n - t;
  for (int i = 0; i < n; i++) {
    if (cnt2 == 0) {
      break;
    }
    if (a[i] == b[i]) {
      cnt2--;
      s[i] = a[i];
    }
  }
  int aa = 0, bb = 0;
  for (int i = 0; i < n; i++) {
    if (s[i]) continue;
    char temp = 'a';
    if (a[i] != b[i]) {
      if (cnt2 > 0) {
        if (aa == 0) {
          s[i] = a[i];
          aa = 1;
        } else {
          s[i] = b[i];
          aa = 0;
          cnt2--;
        }
      } else {
        while (temp == a[i] || temp == b[i]) temp++;
        s[i] = temp;
      }
    } else {
      if (cnt2 > 0) {
        s[i] = a[i];
        cnt2--;
      } else {
        while (temp == a[i] || temp == b[i]) temp++;
        s[i] = temp;
      }
    }
  }
  printf("%s\n", s);
  return 0;
}