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:
#include <iostream>
#include <cmath>
#include <cstdio>
#include <cassert>
#define REP(i,s,n) for(int i=s;i<n;++i)
#define rep(i,n) REP(i,0,n)
using namespace std;
double ans,ko,hen,san,theta;
int n,k;
int main() {
  cin >> n >> k;
  ko = M_PI/(double)n - sin(2*M_PI/(double)n)/2;
  hen = sqrt(2-2*cos(2*M_PI/(double)n));
  theta = M_PI*((double)n-2)*((double)k-1)/((double)n)/((double)n-2);
  san = hen/2*tan(theta)*hen/2;
  ans = M_PI - ko*n - san*n;
  //cout << ko << ',' << hen << ',' << theta << ',' << san;                                                                                                                        
  //cout << ans << endl;                                                                                                                                                           
  printf("%.9f\n",ans);
  return 0;
}