Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
P. Area of a Star

time limit per test

0.5 secondsmemory limit per test

64 megabytesinput

standard inputoutput

standard outputIt 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* < 10^{9}, *n* is prime) and *r* (1 ≤ *r* ≤ 10^{9}) — 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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/02/2021 08:46:23 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|