The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).

The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.

A person can move from one cell to another if those cells are not occupied by hotels and share a side.

Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?

Input

The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.

Output

Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".

If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.

Examples

Input

7 2


Output

YES
.......
.#.....
.#.....
.......


Input

5 3


Output

YES
.....
.###.
.....
.....
#include <bits/stdc++.h>
using namespace std;
const int INF = 0x7ffffff;
const int MAXN = +3;
int n, k;
int main() {
  cin >> n >> k;
  if (!(k % 2)) {
    cout << "YES" << endl;
    for (int i = 0; i < n; i++) cout << ".";
    cout << endl;
    cout << ".";
    for (int i = 0; i < k / 2; i++) cout << "#";
    for (int i = 0; i < n - 1 - k / 2; i++) cout << ".";
    cout << endl;
    cout << ".";
    for (int i = 0; i < k / 2; i++) cout << "#";
    for (int i = 0; i < n - 1 - k / 2; i++) cout << ".";
    cout << endl;
    for (int i = 0; i < n; i++) cout << ".";
  } else {
    if (n > 3 && k == (n - 2) * 2 - 1) {
      cout << "YES\n";
      for (int i = 0; i < n; i++) cout << ".";
      cout << endl << ".";
      for (int i = 0; i < n - 2; i++) cout << "#";
      cout << "." << endl << ".";
      for (int i = 0; i < n / 2 - 1; i++) cout << "#";
      cout << ".";
      for (int i = 0; i < n / 2 - 1; i++) cout << "#";
      cout << "." << endl;
      for (int i = 0; i < n; i++) cout << ".";
    } else if (k == 1) {
      cout << "YES\n";
      for (int i = 0; i < n; i++) cout << ".";
      cout << endl;
      for (int i = 0; i < n / 2; i++) cout << ".";
      cout << "#";
      for (int i = 0; i < n / 2; i++) cout << ".";
      cout << endl;
      for (int i = 0; i < n; i++) cout << ".";
      cout << endl;
      for (int i = 0; i < n; i++) cout << ".";
    } else {
      cout << "YES" << endl;
      for (int i = 0; i < n; i++) cout << ".";
      cout << endl;
      for (int i = 0; i < n - (k - 3) / 2 - 4; i++) cout << '.';
      for (int i = 0; i < (k - 3) / 2; i++) cout << '#';
      cout << "#.#.\n";
      for (int i = 0; i < n - (k - 3) / 2 - 4; i++) cout << '.';
      for (int i = 0; i < (k - 3) / 2; i++) cout << '#';
      cout << "#...\n";
      for (int i = 0; i < n; i++) cout << ".";
    }
  }
  return 0;
}
