Problem Statement

You want to create one grid whose number of rows equals its number of columns, and paint exactly $N$ of its cells black.
However, the number of black cells in any single row or column must be at most $K$.
Output the minimum number of rows of the grid, and then output which cells should actually be painted black with that number of rows.

Input

$N\ K$

$1 \le K \le N \le 1000$
$K$ and $N$ are integers

Output

Output in the following format.

$M$
$A_{1,1}A_{1,2}A_{1,3}\dots A_{1,M}$
$A_{2,1}A_{2,2}A_{2,3}\dots A_{2,M}$
$A_{3,1}A_{3,2}A_{3,3}\dots A_{3,M}$
$\hspace{7pt} \vdots \hspace{17pt} \vdots \hspace{16pt} \vdots \hspace{9pt} \ddots \hspace{8pt} \vdots$
$A_{M,1}A_{M,2}A_{M,3}\dots A_{M,M}$

Sample

8 2

4
##..
##..
..##
..##

5 1

5
#....
....#
...#.
.#...
..#..