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.