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
.....
.###.
.....
.....
s = input().split()
n, k = int(s[0]), int(s[1])
count = k
cl = []

if k%2==0:
 p = k//2
 for x in range(4):
  t = []
  for y in range(n):
   if count!=0:
    if y<=p and y>0 and x<4 and x>0:
     t.append('#')
     count-=1
    else:
     t.append('.')
   else:
    t.append('.')
  cl.append(t)
else:
 centr = n//2
 p = k%(n-2)
 if p==k:
  p1 = k//2
  p2 = 0
 else:
  p1 = (n-2)//2
  p2 = k%(n-2)
 p2 = p2//2
 for x in range(4):
  t = []
  for y in range(n):
   if count != 0:
    if y <= centr+p1 and y >= centr-p1 and x == 1:
     t.append('#')
     count -= 1
    elif y>0 and (y <= p2 or y > n-2-p2) and y<n-1 and x == 2:
     t.append('#')
     count -= 1
    else:
     t.append('.')
   else:
    t.append('.')
  cl.append(t)

res = ''
for x in range(4):
 for y in range(n+1):
  if y==n:
   res+='\n'
  else:
   res+=cl[x][y]

print('YES')
print(res)