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
.....
.###.
.....
.....
col, hotel = map(int, input().split())
if (col-2) * 2 < hotel:
    print("NO")
else:
    print("YES")
    if hotel % 2 == 0:
        hotel_col = hotel//2
        print("." * col)
        print("." + "#"*hotel_col + "."*(col-1-hotel_col))
        print("." + "#"*hotel_col + "."*(col-1-hotel_col))
        print("."*col)
    else:
        if hotel <= col - 2:
            print("." * col)
            print("."*((col-hotel)//2) + "#"*hotel + "."*((col-hotel)//2))
            print("."*col) 
            print("."*col)  
        else:
            hotel_col = hotel - col + 2
            print("." * col)
            print("." + "#"*(col - 2) + ".")
            print("."*((col-hotel_col-1)//2) + "#"*(hotel_col//2)+"."+ "#"*(hotel_col//2) + "."*((col-hotel_col-1)//2))
            print("."*col)  