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 ri with 1 ≤ ri ≤ 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
anshuman16423: 2018-12-04 12:04:42

Wasted 2hr for not incrementing f :P

ayush251196: 2018-10-25 21:02:18

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

mujahid_3732: 2018-10-13 19:22:53

1st time AC in one go ...

sudhanshu6324: 2018-08-22 09:42:47

1st time AC in one go

sudhanshu6324: 2018-08-22 09:12:18

anybody please explain the test cases

derek_69: 2018-07-26 20:31:34

use printf

karan_yadav: 2018-07-07 14:42:06

Never gave it a thought that we can use BS in decimal values as well!!!
Nice problem. For me, better than aggressive cows :)

cosmicray001: 2018-06-07 12:49:00

@Shafaet, if you use to write code in c/c++, then double pi = acos(-1.0);

ankur314: 2018-05-14 16:10:31

use pi as acos(-1). Gave 3 WAs even when i manually took a precise value of pi but acos(-1) gave AC..

mr_nair: 2018-01-08 23:37:54

make sure pi is also declared double, got me TLE.


Added by:overwise
Date:2007-10-02
Time limit:0.751s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM ICPC NWERC 2006