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

#########
........#
#########
#........
#########
........#
#########
#........
#########
import math
import itertools

gh = lambda: map( int, input().split() )

def main():
    n, m = gh()
    x, y = 1, 1    
    arr = [['.' for i in range(m + 1)] for j in range(n + 1)]
    while x <= n:
        if x % 4 == 1:
            while y <= m:
                arr[x][y] = '#'
                y += 1
            y = m
        else:
            while y > 0:
                arr[x][y] = '#'
                y -= 1
            y = 1
        if x != n:
            arr[x + 1][y] = '#'
        x += 2
    for i in range( 1, n + 1 ):
        for j in range( 1, m + 1 ):
            print( arr[i][j], end="" )
        print()
main()