2455. Cylinder

单点时限: 2.0 sec

内存限制: 256 MB

Using a sheet of paper and scissors, you can cut out two faces to form a cylinder in the following way:

  1. Cut the paper horizontally (parallel to the shorter side) to get two rectangular parts.

  2. From the first part, cut out a circle of maximum radius. The circle will form the bottom of the cylinder.

  3. Roll the second part up in such a way that it has a perimeter of equal length with the circle’s circumference, and attach one end of the roll to the circle. Note that the roll may have some overlapping parts in order to get the required length of the perimeter.

Given the dimensions of the sheet of paper, can you calculate the biggest possible volume of a cylinder which can be constructed using the procedure described above?

输入格式

The input consists of several test cases. Each test case consists of two numbers w and h (1 ≤ w ≤ h ≤ 100), which indicate the width and height of the sheet of paper.

The last test case is followed by a line containing two zeros.

输出格式

For each test case, print one line with the biggest possible volume of the cylinder. Round this number to 3 places after the decimal point.

样例

Input
10 10
10 50
10 30
0 0
Output
54.247
785.398
412.095
hint:
In the first case, the optimal cylinder has a radius of about 1.591549, in the second case, the optimal cylinder has a radius of 5, and in the third case, the optimal cylinder has a radius of about 3.621795.

9 人解决,27 人已尝试。

10 份提交通过,共有 81 份提交。

7.8 EMB 奖励。

创建: 10 年,11 月前.

修改: 2 年,4 月前.

最后提交: 1 月,1 周前.

来源: Ulm Local 2007

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