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 = [int(i) for i in raw_input().split(' ')]
print 'YES'

if k % 2 == 0:
    t = k >> 1
    print '.' * n
    print '.' + '#' * t + '.' * (n - 1 - t)
    print '.' + '#' * t + '.' * (n - 1 - t)
    print '.' * n
else:
    if k <= n - 2:
        t = (n - k) >> 1
        print '.' * n
        print '.' * t + '#' * k + '.' * t
        print '.' * n
        print '.' * n
    else:
        t = 2 * n - k - 4
        u = (n - t - 2) >> 1
        print '.' * n
        print '.' + '#' * (n - 2) + '.'
        print '.' + u * '#' + '.' * t + '#' * u + '.'
        print '.' * n
