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[0])
k = int(n_k[1])

# def factorize(a):
# 	if a == 0 or a == 1:
# 		return 1
# 	ret = 1
# 	for i in range(1, a+1):
# 		ret *= i
# 	return ret 

# def choose(a, b):
# 	return int(factorize(a)/factorize(b)/factorize(a-b))

# def calc(a, b):
# 	if a >= b:
# 		return choose(a, b-1)
# 	else:
# 		return choose(b, a-1)

cnt = 0
res = set()
flag = 0
if k % 2 == 0:
	for i in range(2, 4):
		for j in range(2, 2+int(k/2)):
			res.add((i,j))
elif k % 2 == 1:
	if k <= n-2:
		st = int((n+1)/2-(k-1)/2)
		for j in range(st, st+k):
			res.add((2, j))
	else:
		for j in range(2, n):
			res.add((2, j))
		kk = k-n+2
		# if kk % 2 == 1:
		# 	st = int((n+1)/2-(kk-1)/2)
		# 	for j in range(st, st+kk):
		# 		res.add((3, j))
		# else:
		for j in range(2, int(kk/2)+2):
			res.add((3, j))
		st = n-int(kk/2)
		for j in range(st, n):
			res.add((3, j))



output = ''
for i in range(1, 5):
	for j in range(1, n+1):
		if (i, j) in res:
			output += '#'
		else: output += '.'
	output += '\n'
print('YES')
print(output)
