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Ural Regional School Programming Contest 2011

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B. Football Goal

Time limit: 0.5 second
Memory limit: 64 MB
Problem illustration
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.


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Problem Author: Fedor Fominykh
Problem Source: Ural Regional School Programming Contest 2011
To submit the solution for this problem go to the Problem set: 1874. Football Goal