Beavergnaw

Time limit1sMemory limit128 MB

Summary

Given a cylinder of diameter D and height D, find the inner cylinder diameter d so that the remaining wood (two frustums plus a middle cylinder) has the requested volume. Output d to three decimals for each test case.

Level: Medium7 of 10
Topics: Geometry, Math, Binary search
Solved: No attempts yet

Problem

When a beaver gnaws a tree, it cuts a very specific shape out of the trunk. What is left of the trunk looks like two frustums of a cone joined by a cylinder whose diameter equals its height. A very curious beaver, trying not to topple the tree, wants to work out what the diameter of that joining cylinder should be so that he gnaws out a given amount of wood. Help him with the calculation.

Consider an idealized beaver gnawing an idealized tree. Assume the trunk is a cylinder of diameter $D$ , and that the beaver works on a segment of the trunk whose height is also $D$ . What should the diameter $d$ of the inner cylinder be so that the beaver gnaws out exactly $V$ cubic units of wood?

Input

The input contains several test cases, one per line. Each line has two integers $D$ and $V$ separated by whitespace, where $D$ is given in linear units and $V$ in cubic units. $V$ never exceeds the maximum volume of wood the beaver can gnaw out. The line with $D = 0$ and $V = 0$ marks the end of the input and must not be processed.

Output

For each test case, print one line containing the value of $d$ , measured in linear units, rounded to exactly three digits after the decimal point.

Examples4

Example 1

Input

Expected output

Example 2
Input
```
1 0
0 0
```
Expected output
```
1.000
```
Example 3
Input
```
10 0
0 0
```
Expected output
```
10.000
```
Example 4
Input
```
5 10
7 20
3 1
0 0
```
Expected output
```
4.731
6.730
2.928
```