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
sujay008:
20200603 18:02:35
can someone explain the test case.


ghost_code_24:
20200601 22:55:38
If not clicking, try reading about binary search on monotonic functions. 

shash_mehul02:
20200310 13:19:01
Problem where you need to think against the general opinion that you get on the first go. 

shashwat_07:
20200115 11:06:26
Nice problem!! Involves binary search on floating values. 

syed_tanveer:
20190404 14:41:46
A nice problem. Taught the concept of binary search on a monotonic function. 

aashkumar5:
20190220 08:10:32
use double don't use float. I don't know why.. but float got me TLE. 

anshuman16423:
20181204 12:04:42
Wasted 2hr for not incrementing f :P 

ayush251196:
20181025 21:02:18
I used printf("%.4Lf\n",m) instead of printf("%.4f\n",m) and got an AC!! Wats happening?? 

mujahid_3732:
20181013 19:22:53
1st time AC in one go ... 

sudhanshu6324:
20180822 09:42:47
1st time AC in one go

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 