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
.....
.###.
.....
.....
n,k=map(int,input().split())
a=[]
for i in range(4):
    b=[]
    for j in range(n):
        b.append('.')
    a.append(b)
if k%2==0:
    print("YES")
    q=k//2

    for i in range(1,q+1):
        a[1][i]='#'
        a[2][i]='#'
    for i in a:
        for j in i:
            print(j,end="")
        print()
elif k<=n-2:
    print("YES")
    print('.'*n)
    print('.'*((n-k)//2)+k*'#'+'.'*((n-k)//2))
    print('.' * n)
    print('.' * n)
else:
    print("YES")
    print('.' * n)
    print('.'+(n-2)*'#'+'.')
    print('.'+'#'*((k-n+2)//2)+'.'*((2*n-k-4))+'#'*((k-n+2)//2)+'.')
    print('.' * n)