PIE - Pie

题面翻译

描述 我的生日要到了！根据习俗，我需要将一些派分给大家。我有N个不同口味、不同大小的派。有F个朋友会来参加我的派对，每个人会拿到一块派（必须一个派的一块，不能由几个派的小块拼成；可以是一整个派）。

我的朋友们都特别小气，如果有人拿到更大的一块，就会开始抱怨。因此所有人拿到的派是同样大小的（但不需要是同样形状的），虽然这样有些派会被浪费，但总比搞砸整个派对好。当然，我也要给自己留一块，而这一块也要和其他人的同样大小。

请问我们每个人拿到的派最大是多少？每个派都是一个高为1，半径不等的圆柱体。

输入 第一行包含一个整数，表示测试个数。 对于每个测试，第一行两个正整数N和F，1 ≤ N, F ≤ 10 000，表示派的数量和朋友的数量。 第二行包含N个1到10000之间的整数，表示每个派的半径。 输出 输出每个人能得到的最大的派的体积，精确到小数点后三位。

题目描述

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.

输入格式

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.

输出格式

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 $^{-3}$ .

样例 #1

样例输入 #1

3
3 3
4 3 3
1 24
5
10 5
1 4 2 3 4 5 6 5 4 2

样例输出 #1

25.1327
3.1416
50.2655