Ural 1874 Football Goal

1874. Football Goal

Time limit: 0.5 second
Memory limit: 64 MB

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.

Input

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

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.

Sample

inputoutput

2 2

4.828427125

Problem Author: Fedor Fominykh
Problem Source: Ural Regional School Programming Contest 2011

题意：

有一棵无限高的树，还有两个长度为a,b的棍子，用这棵树和一根棍子作为门的两侧门框，另一个棍子作为门的上横梁，求最大门的面积，门为四边形且可以不规则。

嗯，就是这样……

代码：

import java.util.Scanner;public class Main {public static void main(String args[]) {Scanner Cin = new Scanner(System.in);double a = Cin.nextDouble();double b = Cin.nextDouble();double re = (a * a + b * b) / 4.0 + Math.sqrt(2.0) / 2 * a * b;System.out.printf("%.8f\n",re);System.out.println();}}