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())
ans = [['.' for j in range(n)] for i in range(4)]
if (k % 2 == 0):
    for j in range(1, k // 2 + 1):
        ans[1][j] = ans[2][j] = '#'
    print("YES")
    for i in range(4):
        print(*ans[i], sep = '')
else:
    if (n % 2 == 1):
        ans[1][n // 2] = '#'
        k -= 1
        t = min(n - 3, k)
        for j in range(1, t // 2 + 1):
            ans[1][j] = ans[1][n - j - 1] = '#'
        k -= t
        
        for j in range(1, k // 2 + 1):
            ans[2][j] = ans[2][n - j - 1] = '#'
        print('YES')
        for i in range(4):
            print(*ans[i], sep = '')
    else:
        print('NO')
    
