PIE  Pie
My birthday is coming up and traditionally I'm serving pie. Not just one pie, no, I have a number N of them, of various tastes and of various sizes. F of my friends are coming to my party and each of them gets a piece of pie. This should be one piece of one pie, not several small pieces since that looks messy. This piece can be one whole pie though.
My friends are very annoying and if one of them gets a bigger piece than the others, they start complaining. Therefore all of them should get equally sized (but not necessarily equally shaped) pieces, even if this leads to some pie getting spoiled (which is better than spoiling the party). Of course, I want a piece of pie for myself too, and that piece should also be of the same size.
What is the largest possible piece size all of us can get? All the pies are cylindrical in shape and they all have the same height 1, but the radii of the pies can be different.
Input
One line with a positive integer: the number of test cases. Then for each test case:
 One line with two integers N and F with 1 ≤ N, F ≤ 10000: the number of pies and the number of friends.
 One line with N integers r_{i} with 1 ≤ r_{i} ≤ 10000: the radii of the pies.
Output
For each test case, output one line with the largest possible volume V such that me and my friends can all get a pie piece of size V. The answer should be given as a floating point number with an absolute error of at most 10^{3}.
Example
Input: 3 3 3 4 3 3 1 24 5 10 5 1 4 2 3 4 5 6 5 4 2 Output: 25.1327 3.1416 50.2655
hide comments
agaurav77:
20150927 10:16:49
Shafaet is right, WAs may occur due to an imprecise value of Pi, use a significantly precise value like he gave. AC :) 

Devashish:
20150905 00:27:08
Size same by volume of the pie or area of the pie(considering horizontal cuts are not valid)? help? 

Utsav Sinha:
20150809 16:01:51
Used double and got ac in C 

chinmay rakshit:
20150701 07:12:56
binary search on monotonic increasing function.... nlogn. 

Shafaet:
20110322 14:58:58
I was getting precision error,then i used long double and Pi=3.14159265358979323846264338327950 and got ac. 
Added by:  overwise 
Date:  20071002 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  ACM ICPC NWERC 2006 