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 = [int(i) for i in input().split()]
st = []
for i in range(4):
	st.append([])
	for j in range(n):
		st[i].append(".")
if (k % 2 == 0) and (k // 2 <= (n - 2)):
	for i in range(1, n - 1):
		if k == 0:
			break
		for j in range(1,3):
			if k == 0:
				break
			st[j][i] = "#"
			k -= 1
elif (k >= (n - 2)):
	for i in range(1, n - 1):
		st[1][i] = "#"
	if k >= n:
		st[2][1] = "#"
		st[2][n - 2] = "#"
		for i in range(2, k - n + 2):
			st[2][i] = "#"
	if k == n - 1:
		st[2][(n - 2) // 2] = "#"
else:
	wk1 = (n - 2) // 2
	for i in range(wk1 - k // 2 + 1, wk1 + k // 2 + 2):
		st[1][i] = "#"
print("YES")
for i in range(4):
	for j in range(n):
		print(st[i][j], end = "")
	print()

	
