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
.....
.###.
.....
.....
#!/usr/bin/env python3

[n, k] = map(int, input().strip().split())

res = [['.' for _ in range(n)] for __ in range(4)]

l = 1
r = n - 2
c = (n - 1) // 2
while k >= 4:
	for i in [1, 2]:
		for j in [l, r]:
			res[i][j] = '#'
	l += 1
	r -= 1
	k -= 4

if k > 0:
	res[1][c] = '#'
if k == 2:
	res[2][c] = '#'
if k == 3:
	res[1][c - 1] = '#'
	res[1][c + 1] = '#'

print ('YES')
for row in res:
	print (''.join(row))
