Code in C++ please:

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 (3n,m50).

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

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