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
.....
.###.
.....
.....
#!/usr/bin/env python3
# -*- encoding: utf-8 -*-

import sys

def print_list(l):
    for e in l:
        print("".join(e))
    return

def main():
    n,k = map(int,sys.stdin.readline().strip().split())
    grid = [['.' for _ in range(n)] for _ in range(4)]

    q = k//2
    r = k %2

    if r == 0:
        for i in range(q):
            grid[1][i+1] = "#"
            grid[2][i+1] = "#"
        print("YES")
        print_list(grid)
    else:
        for i in range(q):
            grid[1][i+1] = "#"
            grid[1][n-(i+2)] = "#"
        if k > n-2:
            reste = k-(n-2)
            for i in range(reste//2):
                grid[2][i+1] = "#"
                grid[2][n-(i+2)] = "#"
        else:
            grid[2][n//2] = '#'

        print("YES")
        print_list(grid)


main()
