Sonichka's Birthday

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 $m$ ($3\le n,m\le 1000$) — the height and width, respectively.

Output

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

Examples