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 = list(map(int, input().split()))
t = [(['.'] * n ) for i in range(4)]
if k%2==1:
	t[1][n//2] = '#'
	k -= 1
if k == 2*(n-2):
	t[2][n//2] = '#'
	t[1][n//2] = '#'
	k -= 2
#print(t, k)
if k > (n-3):
	for i in range(1, n-1):
		if i != n//2:
			t[2][i] = '#'
			k -= 1
#print(t, k)
for i in range(k//2):
	t[1][i+1] = '#'
	t[1][n-i-2] = '#'
k = k % 2
#print(t, k)

print('YES')
#print(t)
print('\n'.join([''.join(i) for i in t]))
	
