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
.....
.###.
.....
.....
import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class B {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        // Scanner scan = new Scanner(System.in);
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        // int n = Integer.parseInt(bf.readLine());
        StringTokenizer st = new StringTokenizer(bf.readLine());
        // int[] a = new int[n]; for(int i=0; i<n; i++) a[i] = Integer.parseInt(st.nextToken());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        out.println("YES");
        char[][] grid = new char[4][n];
        for(int i=0; i<4; i++) Arrays.fill(grid[i], '.');
        if(k % 2 == 1) {
          grid[1][n/2] = '#';
          k--;
        }
        for(int i=1; i<=n/2; i++) {
          for(int j=1; j<=2; j++) {
            if(k > 0) {
              grid[j][i] = '#';
              grid[j][n-1-i] = '#';
              if(i == (n-1-i)) k -= 1;
              else k -= 2;
            }
          }
        }
        for(int i=0; i<4; i++) {
          StringBuilder sb = new StringBuilder();
          for(int j=0; j<n; j++) sb.append(grid[i][j]);
          out.println(sb.toString());
        }
        // int n = scan.nextInt();

        out.close(); System.exit(0);
    }
}
