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())

if k % 2 == 0:
    print("YES")
    k1 = k // 2
    k2 = k // 2
    for x in range(4):
        for y in range(n):
            if (x == 1 and y > 0 and y < n - 1) and k1 > 0:
                print('#', end = '')
                k1 -= 1
            elif (x == 2 and y > 0 and y < n - 1) and k2 > 0:
                print('#', end = '')
                k2 -= 1
            else:
                print('.', end = '')
        print()
else:
    print("YES")
    if k > n - 2:
        k -= 1
        for x in range(4):
            for y in range(n):
                if x == 1 and y > 0 and y < n - 1:
                    print('#', end = '')
                    k -= 1
                elif x == 2 and y == n - 2:
                    print('#', end = '')
                elif x == 2 and y > 0 and k > 0:
                    print('#', end = '')
                    k -= 1
                else:
                    print('.', end = '')
            print()
    else:
        s = n // 2
        d = k // 2
        for x in range(4):
            for y in range(n):
                if x == 1 and abs(s - y) <= d:
                    print('#', end = '')
                else:
                    print('.', end = '')
            print()
                
