Golden section

Time Limit: 1000 ms

Memory Limit: 65535 ms


It’s known to all that thinking is good at geometry.Fishhead has a problem to him today, make a cylinder in fishhead’s way!

Using a sheet of paper and scissors, you can cut out two faces to form a cylinder in the fishhead’s 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.

Busy as thinking is ,he ask you to fininsh this task.

Given the dimensions of the sheet of paper, can you calculate the biggest possible volume of a cylinder which can be constructedin the fishhead’s way?


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.


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.

Sample Input

10 10
10 50
10 30
0 0

Sample Output

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.