Sonichka's Birthday
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$3 \leq n, m \leq 1\,000$$$) — the height and width, respectively.

Output

Output the ornament of size $$$n \times m$$$.

Examples

Input

    6 4

Output

    x..x
    .xx.
    .xx.
    x..x
    .xx.
    .xx.

Input

    12 5

Output

    x...x
    .x.x.
    ..x..
    .x.x.
    x...x
    .x.x.
    ..x..
    .x.x.
    x...x
    .x.x.
    ..x..
    .x.x.

Input

    21 12

Output

    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..