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 math
from collections import *
from string import *
from fractions import *

n,k = map(int,raw_input().strip().split())
grid = [['.']*n for i in range(4)]

def display(grid):
    for i in grid:
        print "".join(i)
    
if k>(n-1)**2:
    print "NO"
else:
    ans = "YES"
    if k&1:
        if k>=(n-2):
            for i in range(1,n-1):
                grid[1][i] = "#"
            k -= (n-2)    
        offset = 1
        if k&1:
            grid[2][n/2] = "#"
            k -= 1
        for i in range(k/2):
            grid[2][n/2 - offset] = "#"
            grid[2][n/2 + offset] = '#'
            offset += 1
            k -= 2
         
    else:
        row = 1
        col = n-2
        while k>0:
            grid[row][col] = "#"
            k -= 1
            if row==2:
                col -= 1
            if row==2: row = 1
            else: row = 2
    print ans
    if ans == "YES":
        display(grid)