Unlike most students of the Mathematical Department, Sonya is fond of not
only programming but also sports. One fine day she went to play football
with her friends. Unfortunately, there was no football field anywhere
around. There only was a lonely birch tree in a corner of the yard. Sonya
searched the closet at her home, found two sticks, and decided to
construct a football goal using the sticks and the tree. Of course, the
birch would be one of the side posts of the goal. It only remained to make
the other post and the crossbar.
Sonya wanted to score as many goals as possible, so she decided to
construct a goal of maximum area. She knew that the standard football goal
was rectangular, but, being creative, she assumed that her goal could have
the form of an arbitrary quadrangle.
You can assume that the birch tree is a segment of a straight line
orthogonal to the ground.
The only line contains integers a and b, which are the lengths of the
sticks (1 ≤ a, b ≤ 10 000). It is known that the total length of
the sticks is less than the height of the birch tree.
Output the maximum area of the goal that can be constructed with the use
of the sticks and the birch tree. The answer must be accurate to at least
six fractional digits.
Problem Author: Fedor Fominykh
Problem Source: Ural Regional School Programming Contest 2011