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(" "))

if k%2 == 0:
    print "YES"
    print '.'*n
    a = '.'
    for i in xrange(n-2):
        if i < k/2:
            a += '#'
        else:
            a += '.'
    a += '.'

    print a
    print a
    print '.'*n
elif k != n-1:
    print "YES"
    print '.' * n
    if k <= n-2:
        print '.' * ((n-k)/2) + '#'*k + '.' * ((n-k)/2)
        print '.' * n
    else:
        print '.' + '#'*(n-2) + '.'
        print '.#' + '#' * (k-(n-2)-2) + '.'*(n-(k-(n-2)+2)) + '#.'
    print '.' * n
else:
    print "NO"


#(n-2) + (n-2)/2+1
#3*(n-2) / 2 + 1

#3n