CodeForces P. Area of a Star【计算几何】

P. Area of a Star

time limit per test

0.5 seconds

memory limit per test

64 megabytes

input

standard input

output

standard output

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 r n 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.

Examples

input

7 10

output

108.395919545675

题意：

给出圆形中的一个n角星，求其面积

题解：

只需要求出黄色三角形的面积，首先可以求出三个角的值，正弦定理可以得到三边长度，面积公式求面积，最后乘上2n即可。

#include<stdio.h>#include<math.h>#define pi acos(-1.0)int main(){    double n,r;    while(~scanf("%lf%lf",&n,&r))    {        double A,B,C,a,c,s;//大写为角，小写为边        A=pi/(2.0*n);//最小的角        B=2*A;//次小的角        C=pi-A-B;//最大角        c=r;//最长边        a=c*sin(A)/sin(C);//正弦定理求出最短的边        s=0.5*a*r*sin(B);//黄色三角形的面积        printf("%.8f\n",2*n*s);    }    return 0;}