Fox Ciel starts to learn programming. The first task is drawing a fox! However, that turns out to be too hard for a beginner, so she decides to draw a snake instead.

A snake is a pattern on a n by m table. Denote c-th cell of r-th row as (r, c). The tail of the snake is located at (1, 1), then it's body extends to (1, m), then goes down 2 rows to (3, m), then goes left to (3, 1) and so on.

Your task is to draw this snake for Fox Ciel: the empty cells should be represented as dot characters ('.') and the snake cells should be filled with number signs ('#').

Consider sample tests in order to understand the snake pattern.

Input

The only line contains two integers: n and m (3 ≤ n, m ≤ 50). 

n is an odd number.

Output

Output n lines. Each line should contain a string consisting of m characters. Do not output spaces.

Examples

Input

3 3


Output

###
..#
###


Input

3 4


Output

####
...#
####


Input

5 3


Output

###
..#
###
#..
###


Input

9 9


Output

#########
........#
#########
#........
#########
........#
#########
#........
#########
def build_snake_matrix(n, m):
    matrix = [["." for _ in range(m)] for _ in range(n)]
    i = 0
    j = 0
    while True:
        # draw line
        for jj in range(m):
            matrix[i][jj] = "#"
        j = m - 1 if j == 0 else 0
        # can I go down?
        if i < n - 2:
            for ii in range(i, i + 3):
                matrix[ii][j] = "#"
            i += 2
        else:
            break

    return matrix


def print_matrix(matrix):
    for row in matrix:
        for el in row:
            print(el, end="")
        print()


def draw_snake(n, m):
    snake = build_snake_matrix(n, m)
    print_matrix(snake)


def main():
    n, m = list(map(int, input().split()))
    draw_snake(n, m)

if __name__ == "__main__":
    main()
