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().strip().split())

grid = [['.' for i in xrange(n)] for j in xrange(4)]

if k & 1:
    q, col = 0, 1
    row = 1
    if k <= n - 2:
        q = (k - 1) // 2
        col = n // 2 - q

    for j in xrange(col, col + min(k, n - 2)): grid[row][j] = '#'
    
    z = k - (n - 2)
    
    st, en = 1, n - 2
    turn = 0
    filled = 0
    while filled < z:
        if turn:
            grid[2][en] = '#'
            en -= 1
        else:
            grid[2][st] = '#'
            st += 1
        
        filled += 1
        turn ^= 1

else:
    for i in xrange(1, 3):
        for j in xrange(1, (k // 2) + 1):
            grid[i][j] = '#'

print "YES"
for i in xrange(4):
    print ''.join(grid[i])