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, input().split())

if k > (2 * (n-1)):
  print("NO")
  
elif k % 2 == 0:
  a1 = "." * n
  a4 = "." * n
  a2 = "." + "#" * int(k/2) + "." * int((n - k/2)-1)
  a3 = "." + "#" * int(k/2) + "." * int((n - k/2)-1)
  
  print("YES")
  print(a1)
  print(a2)
  print(a3)
  print(a4)

elif k <= n-2:
  a1 = "." * n
  a4 = "." * n
  a2 = "." * int((n-k)/2) + "#" * k + "." * int((n-k)/2)
  a3 = "." * n
  
  print("YES")
  print(a1)
  print(a2)
  print(a3)
  print(a4)
  
elif k == n - 1:
  print("NO")

else:
  a1 = "." * n
  a4 = "." * n
  a2 = "." + "#" * int(min(n-2, k)) + "." * ((n-1) - min(n-2, k))
  a3 = "." + "#" + "#" * (k - (a2.count("#") + 2)) + "." * (2 * (n-2) - k) + "#" +"."
  
  print("YES")
  print(a1)
  print(a2)
  print(a3)
  print(a4)