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
.....
.###.
.....
.....


def solve():
    num_columns, num_hotels = (int(x) for x in input().split())


    grid = [['.' for _ in range(num_columns)] for _ in range(4)]

    if num_hotels % 2 == 1:
        if num_hotels > num_columns - 2:
            half_num_hotels = (num_hotels + 1) // 2
            middle = num_columns // 2
            for col in range(1, 1 + half_num_hotels):
                grid[1][col] = grid[2][col] = '#'
            grid[1][2] = '.'
        else:
            half_num_hotels = (num_hotels + 1) // 2
            middle = num_columns // 2
            for diff in range(half_num_hotels):
                grid[1][middle - diff] = grid[1][middle + diff] = '#'
    else:
        num_full_columns = num_hotels // 2
        for col in range(1, 1 + num_full_columns):
            grid[1][col] = grid[2][col] = '#'

    print('YES')
    for grid_row in grid:
        print(*grid_row, sep='')


solve()
