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
.....
.###.
.....
.....
from sys import stdin

n, k = map(int, stdin.readline().split())
out = [['.'] * n for _ in range(4)]
if k & 1:
    out[1][n >> 1] = '#'
    k -= 1

for i in range(1, 3):
    l, r = 1, n - 2
    for j in range(1, n - 2):
        if k:
            k -= 1
            if j & 1:
                out[i][l] = '#'
                l += 1
            else:
                out[i][r] = '#'
                r -= 1

for i in range(1, 3):
    if k:
        k -= 1
        out[i][n >> 1] = '#'
print('YES\n%s' % ('\n'.join([''.join(x) for x in out])))
