Problem C: Moon Cake

Problem C: Moon Cake

Time Limit: 1 Sec  Memory Limit: 128 MB  Special Judge
Submit: 2146  Solved: 324
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There are \(n\) students in CS203 DSAA. Dr. Tang has \(m\) moon cakes for students to celebrate the Mid-Autumn Festival. The radius of moon cake are \(r_1, r_2, \dots, r_m\). Dr. Tang hopes every student can get exactly one equal-sized moon cake.

To meet this goal, some moon cakes may be cut. If a moon cake is cut, it is split into two parts and each part can be seemed as a new moon cake.

To make the problem easier, all the moon cake has the same thickness and the cut is legal if and only if the cutting surface is perpendicular to the circular surface.


The first line of the input contains two integers \(n\) and \(m(1 \le n, m \le 10^6)\) ---- the number of students and the number of moon cakes.

The second line contains \(m\) integers \(r_i(1 \le r_i \le 10^3)\) ---- the radius of \(i\)-th moon cake


Print the maximum area of moon cake for each student

Sample Input

12 3
2 2 2

Sample Output



We use speical judge in this problem, i.e., you only need to guarantee abs(your answer - suggested answer) \(\le\) \(10^{-5}\).

本题采用speical judge,当您的答案与正确答案的绝对值不超过 \(10^{-5}\) 时,结果正确。

Note: It is suggestive for you to use Math.floor() in java when you turn the result of double decision into integer. For cpp user, please use printf() to print your answer.