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, input().split())

s = '.' * n

print('YES')

if k % 2 == 0:
    l = k // 2
    print(s)
    x = '.' + l * '#' + (n - l - 1) * '.'
    print(x)
    print(x)
    print(s)
else:
    print(s)
    l = k
    ss = [list(s), list(s)]
    ll = 0
    i = 1
    while l > 0:
        if i == (n - 1) // 2:
            l -= 1
            ss[ll][i] = '#'
            ll += 1
            i = 1
        elif l >= 2:
            l -= 2
            ss[ll][i] = '#'
            ss[ll][n-i-1] = '#'
            if i == (n - 1) // 2:
                ll += 1
            i += 1
        elif l == 1:
            ss[ll][(n-1)//2] = '#'
            l -= 1

    print(''.join(ss[0]))
    print(''.join(ss[1]))
    print(s)
