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())
if k>2*(n-2):
    print("NO")
else :
    print("YES")
    if k%2==0:
        print('.'*n)
        x=k//2
        print('.'+'#'*x+'.'*(n-x-1))
        print('.'+'#'*x+'.'*(n-x-1))
        print('.'*n)
    else :
        print('.'*n)
        if k>n-2:
            print('.'+'#'*(n-2)+'.')
            k-=n-2
            i=1
            j=n-2
            temp=['.']*n
            while k>0:
                temp[i]='#'
                temp[j]='#'
                i+=1
                j-=1
                k-=2
            print(''.join(temp))
        else :
            temp=['.']*n
            temp[n//2]='#'
            k-=1
            i=n//2-1
            j=n//2+1
            while k>0:
                temp[i]='#'
                temp[j]='#'
                k-=2
                i-=1
                j+=1
            print(''.join(temp))
            print('.'*n)
        print('.'*n)