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
.....
.###.
.....
.....
import atexit
import io
import sys

# Buffering IO
_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER

@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
    

def main():
    n, k = [int(x) for x in input().split()]
    print('YES')
    a=  [['.' for x in range(n)] for y in range(4)]
    if k % 2 == 0:
        for i in range(k//2):
            a[1][i +1] = '#'
            a[2][i +1] = '#'
        
    else:
        a[1][n//2] = '#'
        k -= 1
        for i in range(k):
            if i % 2 == 0:
                j = i // 4 + 1
            else:
                j = - (i//4) -2
            if i% 4 in (0,1):
                t = 1
            else: 
                t = 2
            a[t][j] = '#'
            
    for i in range(4):
        print(''.join(a[i]))
    
if __name__ == '__main__':
    main()
        