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, raw_input().split())
ar = [[False for i in xrange(n)] for i in xrange(4)]
s = ''

x = k / 2 
if x % 2 == 1:
  ar[1][n/2] = True
for i in range(1, x/2 +1):
  ar[1][i] = ar[1][n-1-i] = True
k = k - x

if k % 2 == 1:
  k -= 1
  ar[2][n/2] = True

if k > 0:
  for j in range(0, min(k/2, n/2)):
    ar[2][j + 1] = ar[2][n-2-j] = True
    k -= 2

if k > 0:
  print 'NO'
else:
  print "YES"
  for i in xrange(4):
    for j in xrange(n):
      if ar[i][j]:
        s += '#'
      else:
        s += '.'
    s += '\n'
  print s