Pool table (2) P26585

This exercise has the same statement that ‍; the only difference is that now you can use vectors to solve it.

Write a program that reads the dimensions of a pool table, and that prints with zeros the trajectory of a ball after hitting it in the upper left corner with an angle of 45 degrees.

Input

Input consists of several cases, each with the number of rows and the number of columns. Both numbers are, at least, 2. None of the numbers is “too big”.

Output

Print every pool table as shown in the examples, and an empty line after each table.