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
mradul_2212:
20231018 16:12:55
can someone explain me the predicate function used in this question....what's the logic used in finding is possible to distribute m amount of pie among all f+1 friends?


swapnamoy:
20230718 15:00:06
the first on may seem wrong but it is not cause 26 something by dividing equally can come from "3" ones but as there are 4 people 2 26.something cant come from "4" one as it has 5.something radius. all the best. 

kunal972:
20221219 13:46:59
what is value of high?


shnatan:
20221031 10:29:36
Explaining the first test case :


kashipaka123:
20220820 14:33:04
3 3


taejin_101:
20220513 17:19:03
Few things to remember while you code this problem:


nitincp:
20220216 06:06:53
testcase 1


chetan06:
20211231 16:44:19
I don't know why I am getting wrong answer


rajat_jadam:
20210724 15:41:30
epsilon=1e4


nubskr:
20210710 14:24:17
Don't use the standard while loop in binary search, you can't compare doubles here 
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 