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())
str_1 = ''
str_2 = ''
str_3 = ''
str_4 = ''
oryg_k = k
if k == 0:
    print 'YES'
    for x in range(0, n, +1):
        str_1 += '.'
        str_2 += '.'
        str_3 += '.'
        str_4 += '.'
    print str_1
    print str_2
    print str_3
    print str_4
    exit(0)
if k > n*2+2:
    print 'NO'
    exit(0)
if k%2 == 1 and k<=n-2:
    for x in range(0, n, +1):
        str_1 += '.'
        str_3 += '.'
        str_4 += '.'
    for x in range(0, (n-k)/2, +1):
        str_2 += '.'
    for x in range(0, k, +1):
        str_2 += '#'
    for x in range(0, (n-k)/2, +1):
        str_2 += '.'
    for x in range(0, n-len(str_2), +1):
        str_2 += '.'
    print 'YES'
    print str_1
    print str_2
    print str_3
    print str_4
    exit(0)
line_1 = 1
line_2 = 0
while True:
    if k==0:
        break
    if oryg_k - line_1 >= 2:
        if line_1 <= n-4:
            line_1 += 2
            k -=2
            continue
    if line_1 >= n-2:
        if k-line_1 > n-2:
            print 'NO'
            exit(0)
    line_2 = oryg_k-line_1
    break
if line_1 > n-2 or line_2 > n-2:
    print 'NO'
    exit(0)
for x in range(0, n, +1):
    str_1 += '.'
    str_4 += '.'
for x in range(0, (n - line_1) / 2, +1):
    str_2 += '.'
for x in range(0, line_1, +1):
    str_2 += '#'
for x in range(0, (n - line_1) / 2, +1):
    str_2 += '.'
if line_2 == 1:
    for x in range(0, (n - line_2) / 2, +1):
        str_3 += '.'
    for x in range(0, line_2, +1):
        str_3 += '#'
    for x in range(0, (n - line_2) / 2, +1):
        str_3 += '.'
else:
    str_3 += '.#'
    line_2 -=1
    for x in range(2, n-2, +1):
        if line_2 > 1:
            str_3 += '#'
            line_2 -=1
        else:
            str_3 += '.'
    str_3 += '#.'
while True:
    if len(str_2) < n:
        str_2 += '.'
    if len(str_3) < n:
        str_3 += '.'
    if len(str_2) == len(str_3) == n:
        break
print 'YES'
print str_1
print str_2
print str_3
print str_4