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
kshubham02:
20170925 13:00:15
Something is seriously flawed with float in c++. Got 9 TLE using float, changed it to double, immediately AC (well, after 4 attempts at precision). 

lord_poseidon:
20170923 14:16:02
Use precise value of pi 

jatin03:
20170819 14:47:52
Thanks @aditya23 It really means a alot :) 

aditya23:
20170819 14:42:56
Doubles are not floats, so do not compare them !! (Mind It) Last edit: 20170819 14:46:07 

code_aim:
20170610 11:02:31
avoid using cout, instead use printf. 

roukaya_zaki:
20170208 15:49:09
must I calculate the volume of the pie before I began to distribute them?!


ayush5148:
20160826 23:12:23
float costed me 2 WA, use double in c/c++... Last edit: 20160826 23:14:33 

suraj_:
20160822 12:37:28
AC in one go..... 

adichd123:
20160815 12:36:42
use printf please...cout gives WA! 

Akshay Damle:
20160421 16:17:55
Nice question! You don't need long double  double is fine. Just use a precise value of PI. 
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 