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, raw_input().split())

print 'YES'
maps = ["." * n]
for i in xrange(2):
    if k > n - 2:
        result = '.' + (n - 2) * '#' + '.'
        k -= n - 2
    elif k % 2 == 1:
        result = '.' + ((k - 1) / 2) * '#' + ((n - 3) / 2 - ((k - 1) / 2)) * '.' + '#' + ((n - 3) / 2 - ((k - 1) / 2)) * '.' + ((k - 1) / 2) * '#' + '.'
        k = 0
    else:
        result = '.' + ((k) / 2) * '#' + ((n - 3) / 2 - ((k) / 2)) * '.' + '.' + ((n - 3) / 2 - ((k) / 2)) * '.' + ((k) / 2) * '#' + '.'
        k = 0
    maps.append(result)
maps.append('.'*n)
print '\n'.join(maps)