cf-Area of a Star

Area of a Star

Time Limit:500MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

Submit Status

Description

It was decided in IT City to distinguish successes of local IT companies by awards in the form of stars covered with gold from one side. To order the stars it is necessary to estimate order cost that depends on the area of gold-plating. Write a program that can calculate the area of a star.

A "star" figure having n ≥ 5 corners where n is a prime number is constructed the following way. On the circle of radius rn points are selected so that the distances between the adjacent ones are equal. Then every point is connected by a segment with two maximally distant points. All areas bounded by the segments parts are the figure parts.

Input

The only line of the input contains two integers n (5 ≤ n < 10⁹, n is prime) and r (1 ≤ r ≤ 10⁹) — the number of the star corners and the radius of the circumcircle correspondingly.

Output

Output one number — the star area. The relative error of your answer should not be greater than 10^- 7.

Sample Input

Input

7 10

Output

108.395919545675

我们可以求三角形OAB的面积， ∠CAE = 1/2 ∠ COE = PI/n, 那么∠CAO = PI/2n, ∠AOB非常好求, 就是PI/n, 然后AO = r， ∠ABO = PI-∠CAO-∠AOB, 就可以用正弦定理求出任意另外一条边， 然后s = 1/2absinC, 就可以求出来了。

分析如上： 

#include <cmath>
#include <cstdio>
#include <iostream>
#define PI acos(-1.0)
using namespace std;
int main()
{
    int n, r;
    cin>>n>>r;
    double ang1=PI/n/2;
    double ang2=PI/n;
    double ang3=PI-ang1-ang2;
    double fun=r*sin(ang1)/sin(ang3);
    double rec=0.5*fun*r*sin(ang2);
    rec=rec*2*n;
    printf("%.8lf
", rec); 
    return 0;    
}