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A. Fox And Snake

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFox 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

#########

........#

#########

#........

#########

........#

#########

#........

#########

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