1001 Beaver gnaw
Time Limit : 1 Second
Memory limit : 32 Megabyte
Total submit : 84
Accepted : 33
When chomping a tree the beaver cuts a very specific shape out of
the tree trunk. What is left in the tree trunk looks like two
frustums of a cone joined by a cylinder with the diameter the same
as its height. A very curious beaver tries not to demolish a tree
but rather sort out what should be the diameter of the cylinder
joining the frustums such that he chomped out certain amount of
wood. You are to help him to do the calculations.
We will consider an idealized beaver chomping an idealized tree. Let
us assume that the tree trunk is a cylinder of diameter D and that
the beaver chomps on a segment of the trunk also of height D. What
should be the diameter d of the inner cylinder such that the beaver
chomped out V cubic units of wood?
Input
Input contains multiple cases each presented on a separate line.
Each line contains two integer numbers D and V separated by
whitespace. D is the linear units and V is in cubic units. V will
not exceed the maximum volume of wood that the beaver can chomp. A
line with D=0 and V=0 follows the last case.
Output
For each case, one line of output should be produced containing one
number rounded to three fractional digits giving the value of d
measured in linear units.
Sample Input
10 250
20 2500
25 7000
50 50000
0 0
Sample Output
8.054
14.775
13.115
30.901
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