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 MAXN = 123456;
const int MOD = 1e9 + 7;
int n, f, cnt = 0;
bool flag = true, used[MAXN];
char s[MAXN], t[MAXN];
char letter(int pos) {
  for (int i = 'a'; i <= 'z'; ++i) {
    if (s[pos] != i && t[pos] != i) return (char)i;
  }
  return '\0';
}
int main() {
  memset(used, false, sizeof(bool) * MAXN);
  scanf("%d %d\n", &n, &f);
  gets(s);
  gets(t);
  for (int i = 0; i < n; ++i) {
    if (s[i] != t[i]) {
      ++cnt;
    }
  }
  if (ceil(cnt / 2.0) <= f) {
    int Swap = max(0, cnt - f);
    int Change = f - Swap;
    for (int i = 0; i < n && Swap; ++i) {
      if (s[i] != t[i]) {
        if (flag) {
          s[i] = t[i];
          t[i] = '\0';
        } else {
          Swap--;
        }
        flag = !flag;
      }
    }
    for (int i = 0; i < n && Change; ++i) {
      if (s[i] != t[i] && t[i] != '\0') {
        s[i] = letter(i);
        Change--;
      }
    }
    for (int i = 0; i < n && Change; ++i) {
      if (s[i] == t[i]) {
        s[i] = letter(i);
        Change--;
      }
    }
    puts(s);
  } else {
    printf("%d\n", -1);
  }
  return 0;
}