Fox And Snake

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

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

inputFormat

Input

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

n is an odd number.

outputFormat

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

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

样例

9 9

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

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