Problem: Problem

Find the area of ​​a regular N / K polygon inscribed in a circle with a radius of 1.

However, a regular N / K polygon is defined as "the outermost figure that takes N points on the circumference at equal intervals and connects each point every K-1".

For example, a 5/2 polygon can be drawn as follows. First, take five points at equal intervals on the circumference of radius 1.

Sample Input 2 diagram


Next, connect each point every other 2-1 = 1.

Sample Input 2 diagram


The outermost figure is a regular 5/2 square.

Sample Input 2 diagram

Constraints

The input satisfies the following constraints.

* 5 ≤ N ≤ 106
* 1 <K <N / 2
* N and K are integers that are relatively prime

Input

The input is given in the following format.


N K


Two integers N and K are given on one line.

Output

Output the area of ​​a regular N / K polygon inscribed in a circle with a radius of 1 on one line. An error of 10-5 or less is acceptable.

Examples

Input

5 2


Output

1.12256994


Input

20 3


Output

2.93114293


Input

7 3


Output

1.08395920


Input

100000 3


Output

3.14159265

Solution (in CPP):

Solution:
/*  -*- coding: utf-8 -*-
 *
 * 1593.cc: Star
 */

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<iostream>
#include<string>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<list>
#include<queue>
#include<deque>
#include<algorithm>
#include<numeric>
#include<utility>
#include<complex>
#include<functional>
 
using namespace std;

/* constant */

const int MAX_N = 1000000;
const double PI = acos(-1.0);

/* typedef */

template <typename T>
struct Pt {
  T x, y;

  Pt() {}
  Pt(T _x, T _y) : x(_x), y(_y) {}
  Pt(const Pt<T> &pt) : x(pt.x), y(pt.y) {}

  Pt<T> operator+(const Pt<T> pt) const { return Pt<T>(x + pt.x, y + pt.y); }
  Pt<T> operator-() const { return Pt<T>(-x, -y); }
  Pt<T> operator-(const Pt<T> pt) const { return Pt<T>(x - pt.x, y - pt.y); }
  Pt<T> operator*(T t) const { return Pt<T>(x * t, y * t); }
  Pt<T> operator/(T t) const { return Pt<T>(x / t, y / t); }
  T dot(Pt<T> v) const { return x * v.x + y * v.y; }
  T cross(Pt<T> v) const { return x * v.y - y * v.x; }
  Pt<T> mid(const Pt<T> pt) { return Pt<T>((x + pt.x) / 2, (y + pt.y) / 2); }
  T d2() { return x * x + y * y; }
  double d() { return sqrt(d2()); }

  Pt<T> rot(double th) {
    double c = cos(th), s = sin(th);
    return Pt<T>(c * x - s * y, s * x + c * y);
  }

  Pt<T> rot90() { return Pt<T>(-y, x); }

  bool operator==(const Pt<T> pt) const { return x == pt.x && y == pt.y; }
  bool operator<(const Pt<T> &pt) const {
    return x < pt.x || (x == pt.x && y < pt.y);
  }

  void print() { printf("(%lf,%lf)", x, y); }
};

typedef Pt<double> pt;

struct CL {
  pt p;
  double t0, t1;
  CL() {}
  CL(const pt& _p, double _t0, double _t1) : p(_p), t0(_t0), t1(_t1) {}
};

/* global variables */

/* subroutines */

bool cross_lines(const pt& ap, const pt av, const pt& bp, const pt bv, CL& cl) {
  double op01 = av.cross(bv);
  //if (op01 == 0.0) return false; /* need to handle parallel?? */

  if (op01 == 0.0) {
    pt v = bp - ap;
    if (v.cross(av) != 0.0) return false;

    pt a1 = ap + av;
    pt b1 = bp + bv;

    return
      ((bp - ap).dot(b1 - ap) <= 0.0 ||
       (bp - a1).dot(b1 - a1) <= 0.0 ||
       (ap - bp).dot(a1 - bp) <= 0.0 ||
       (ap - b1).dot(a1 - b1) <= 0.0);
  }

  pt v = bp - ap;
  double op0 = v.cross(av);
  double op1 = v.cross(bv);

  double t0 = op1 / op01;
  double t1 = op0 / op01;

  cl.p = bv * t1 + bp;
  cl.t0 = t0;
  cl.t1 = t1;

  return true;
  //return (0.0 <= cl.t0 && cl.t0 <= 1.0 && 0.0 <= cl.t1 && cl.t1 <= 1.0);
}

/* main */

int main() {
  int n, k;
  scanf("%d%d", &n, &k);

  double th = PI * 2 / n;
  pt p0(cos(0.0), sin(0.0)), p1(cos(th), sin(th));
  double s0 = p0.cross(p1) * 0.5;

  double th2 = th * k, th3 = th * (1 - k + n);
  pt p2(cos(th2), sin(th2)), p3(cos(th3), sin(th3));
  CL cl;
  cross_lines(p0, p2 - p0, p1, p3 - p1, cl);
  double s1 = (p0 - cl.p).cross(p1 - cl.p) * 0.5;

  printf("%.8lf\n", (s0 - s1) * n);
  return 0;
}