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 = input().split(' ')
n = int(n)
k = int(k)
print('YES')
if k % 2 == 0:
    k = int(k/2)
    for i in range(1, n+1):
        print('.', end='')
    print()
    print('.', end='')
    for i in range(1, k+1):
        print('#', end='')
    for i in range(1, n-k):
        print('.', end='')
    print()
    print('.', end='')
    for i in range(1, k+1):
        print('#', end='')
    for i in range(1, n-k):
        print('.', end='')
    print()
    for i in range(1, n+1):
        print('.', end='')
else:
    for i in range(1, n+1):
        print('.', end='')
    print()
    if k > n-2:
        print('.', end='')
        for i in range(1, int((n-1)/2)):
            print('#', end='')
        print('.', end='')
        for i in range(1, int((n-1)/2)):
            print('#', end='')
        print('.', end='')
        print()
        for i in range(1, int((2*n-k-3)/2)+1):
            print('.', end='')
        for i in range(1, k-n+4):
            print('#', end='')
        for i in range(1, int((2*n-k-3)/2)+1):
            print('.', end='')
        print()
    else:
        for i in range(1, int((n-k)/2)+1):
            print('.', end='')
        for i in range(1, k+1):
            print('#', end='')
        for i in range(1, int((n-k)/2)+1):
            print('.', end='')
        print()
        for i in range(1, n+1):
            print('.', end='')
        print()
    for i in range(1, n+1):
        print('.', end='')
