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
.....
.###.
.....
.....
nk = input().split(" ")
n,k = int(nk[0]),int(nk[1])

if k == 1:
    print("YES")
    for i in range(4):
            for j in range(n):
                if i == 0 or i == 3 or j == 0 or j == n - 1:
                    print(".",end="")
                else:
                    if i == 1 and j == n // 2:
                        print("#",end="")
                    else:
                        print(".",end="")
            print()
elif k == (n - 2) // 2 + 1:
    print("YES")
    for i in range(n):
        print(".",end="")
    print()
    for i in range(n):
        if i % 2 == 1:
            print("#",end="")
        else:
            print(".",end="")
    print()
    for j in range(2):
            for i in range(n):
                print(".",end="")
            print()
elif k % 2 == 1 and k < n - 2:
    print("YES")
    m = [[0 for i in range(n)] for j in range(4)]
    i = n // 2
    m[1][i] = "#"
    t = k // 2 + 1
    while t > 0:
        m[1][i] = "#"
        i = i + 1
        t = t - 1
    i = n // 2
    t = k // 2 + 1
    while t > 0:
        m[1][i] = "#"
        i = i - 1
        t = t - 1
    for i in range(4):
        for j in range(n):
            if m[i][j] != "#":
                m[i][j] = "."
    for i in range(4):
        for j in range(n):
            print(m[i][j],end="")
        print()
elif k % 2 == 1 and k <= 2* (n - 2) and ((n-2)-(2* (n - 2) -k)) % 2 == 0:
    print("YES")
    for i in range(n):
        print(".",end="")
    print()
    for i in range(n):
        if i == 0 or i == n - 1:
            print(".",end="")
        else:
            print("#",end="")
    print()
    
    k = ((n-2)-(2* (n - 2) -k)) // 2
    print(".",end="")
    for i in range(k):
        print("#",end="")
    for i in range(k,(n - 2) - k):
        print(".",end="")
    for i in range((n-2)-k+1,n-1):
        print("#",end="")
    print(".",end="")
    print()

    for i in range(n):
        print(".",end="")
    print()
else:
    if (k % 2 == 0 or k % (n - 2) == 0) and k <= 2 * (n - 2):
        print("YES")
        if k % (n - 2) == 0:
            for i in range(4):
                for j in range(n):
                    if i == 0 or i == 3 or j == 0 or j == n - 1:
                        print(".",end="")
                    else:
                        if k > 0:
                            print("#",end = "")
                            k = k - 1
                        else:
                            print(".",end="")
                print()
        else:
            m = [[0 for i in range(4)] for j in range(n)]
            for i in range(n):
                for j in range(4):
                    if i == 0 or i == n - 1 or j == 0 or j == 3:
                        m[i][j] = "."
                    else:
                        if k > 0:
                            m[i][j] = "#"
                            k = k - 1
                        else:
                            m[i][j] = "."
            rez = [[m[j][i] for j in range(len(m))] for i in range(len(m[0]))]
            for i in range(4):
                for j in range(n):
                    print(rez[i][j],end="")
                print()
    else:
        print("NO")
                        