Sonichka is Miss M's best friend. She has been admitted to the best university in the distant and progressive country of Noteandia. Unfortunately, Miss M misses her friend very much, so she decided to make a gift for Sonichka while she is studying in another country.
Today is Sonichka's birthday, but since Sonichka will return a bit later, and Miss M has some time, she decided to make a gift.
Miss M decided that she wants to learn cross-stitching and make ornaments on a vishivanka, which will be a gift for Sonichka to give when she returns, but she doesn't know where to start at all. So, she came up with the idea to write a program that will create an ornament of the required width and length, which she can then use as an example for embroidery.
An embroidered shirt is a rectangle $$$n \times m$$$. The ornaments are two rays that come out from the upper corners of the shirt and have angles of $$$45^\circ$$$. The ray reflects when it touches the vertical edge. When the ray touches the bottom edge, it disappears. For a visual example, you can look at the examples below.
Help Miss M learn cross-stitching and give a beautiful embroidered shirt to the lovely Sonichka for her birthday by writing such a program that, given the width $$$n$$$ and length $$$m$$$, will output an example of the ornament.
The first line contains two integers $$$n$$$ and $$$m$$$ ($$$3 \leq n, m \leq 1\,000$$$) — the height and width, respectively.
Output the ornament of size $$$n \times m$$$.
6 4
x..x .xx. .xx. x..x .xx. .xx.
12 5
x...x .x.x. ..x.. .x.x. x...x .x.x. ..x.. .x.x. x...x .x.x. ..x.. .x.x.
21 12
x..........x .x........x. ..x......x.. ...x....x... ....x..x.... .....xx..... .....xx..... ....x..x.... ...x....x... ..x......x.. .x........x. x..........x .x........x. ..x......x.. ...x....x... ....x..x.... .....xx..... .....xx..... ....x..x.... ...x....x... ..x......x..