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 == 1:
    print('YES')
    print('.' * n)
    print('.' * (n // 2),end='')
    print('#',end='')
    print('.' * (n // 2))
    print('.' * n)
    print('.' * n)
else:
    if k % 2 == 0:
        print('YES')
        print('.' * n)
        for i in range(2):
            print('.',end='')
            for i in range(k // 2):
                print('#',end='')
            print('.' * (n - 1 - k // 2))
        print('.' * n)
    else:
        if k % (n - 2) == 0:
            print('YES')
            print('.' * n)
            if k == n - 2:
                print('.',end='')
                print('#' * (n - 2), end='')
                print('.')
                print('.' * (n))
                print('.' * n)
            else:
                print('.',end='')
                print('#' * (n - 2), end='')
                print('.')
                print('#' * (n))
                print('.' * n)
        else:
            if k <= n - 2:
                print('YES')
                print('.' * n)
                for i in range((n - k) // 2):
                    print('.',end='')
                print('#' * k, end='')
                print('.' * ((n - k) // 2))
                print('.' * n)
                print('.' * n)
            else:
                print('YES')
                print('.' * n)
                print('.', end='')
                print('#' * (n - 2), end='')
                print('.')
                print('.', end='')
                print('#' * ((k - n + 2)//2),end='')
                print('.' * (n - 2 - ((k - n + 2)//2) * 2),end='')
                print('#' *((k - n + 2)//2),end='')
                print('.')
                print('.' * n)
                             