#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef int _loop_int;
#define REP(i,n) for(_loop_int i=0;i<(_loop_int)(n);++i)
#define FOR(i,a,b) for(_loop_int i=(_loop_int)(a);i<(_loop_int)(b);++i)
#define FORR(i,a,b) for(_loop_int i=(_loop_int)(b)-1;i>=(_loop_int)(a);--i)

#define DEBUG(x) cout<<#x<<": "<<x<<endl
#define DEBUG_VEC(v) cout<<#v<<":";REP(i,v.size())cout<<" "<<v[i];cout<<endl
#define ALL(a) (a).begin(),(a).end()

#define CHMIN(a,b) a=min((a),(b))
#define CHMAX(a,b) a=max((a),(b))

// mod
const ll MOD = 1000000007ll;
#define FIX(a) ((a)%MOD+MOD)%MOD

// floating
typedef double Real;
const Real EPS = 1e-11;
#define EQ0(x) (abs(x)<EPS)
#define EQ(a,b) (abs(a-b)<EPS)
typedef complex<Real> P;

Real cross(P a,P b){
  return imag(conj(a)*b);
}

Real sur(P a,P b,P c){
  b-=a; c-=a;
  return abs(cross(b,c))/2.0;
}

P ppp[252521];

// count triangle s.t. surface < s
ll calc(int n,Real s){
  Real u = 2.0*M_PI/(Real)n;
  ll ans = 0;
  int a = 0;
  P x = ppp[a];
  ll bai = n;
  if(n%3==0)bai/=3;
  FOR(b,1,n-1){
    P y = ppp[b];
    int low = b+1, high = n-1;
    int cnt = (high-low+1);
    // seisannkakkei guard
    if(n%3==0 && b==n/3){
      cnt--;
    }
    if(cnt%2==1){
      int cent = low + cnt/2;
      P z = ppp[cent];
      if(sur(x,y,z) < s){
        ans += cnt;
        continue;
      }
    }
    cnt /= 2;
    high = low + cnt - 1 + 1;
    low--;
    while(low+1<high){
      int mid = (low+high)/2;
      P z = ppp[mid];
      if(sur(x,y,z) < s){
        low = mid;
      }else{
        high = mid;
      }
    }
    ans += 2ll*(low-b);
  }
  // DEBUG(ans);
  ans /= 3;
  ans *= n;
  return ans;
}

int main(){
  int n;
  ll k;
  cin>>n>>k;
  if(n%3==0 && (ll)n*(n-1)*(n-2)/6 == k){
    puts("1.29903810568");
    return 0;
  }
  Real u = 2.0*M_PI/(Real)n;
  P po = exp(P(0,u));
  ppp[0] = P(1,0);
  REP(i,n)ppp[i+1] = ppp[i]*po;
  Real low = 0.0, high = 1.3;
  // DEBUG(calc(n,2.0));
  REP(_,40){
    Real mid = (low+high)/2.0;
    ll cnt = calc(n,mid);
    // DEBUG(mid);
    // DEBUG(cnt);
    if(cnt >= k){
      high = mid;
    }else{
      low = mid;
    }
  }
  printf("%.12lf\n",low);
  return 0;
}

### Prompt

Please formulate a Cpp solution to the following problem:

Input

The input is given from Standard Input in the following format:


> $N \ K$

Output

* Please output the $K$-th triangle area.
* Print a floating number denoting the answer. The relative or absolute error of your answer should not be higher than $10^{−9}$.



Constraints

* $3 \le N \le 200,000$
* $1 \le K \le \frac{N(N-1)(N-2)}{6}$



Subtasks

Subtask 1 [ $160$ points ]


* $N \le 100$

Subtask 2 [ $240$ points ]


* $N \le 1000$

Subtask 3 [ $450$ points ]


* $N \le 200,000$

Output

* Please output the $K$-th triangle area.
* Print a floating number denoting the answer. The relative or absolute error of your answer should not be higher than $10^{−9}$.



Constraints

* $3 \le N \le 200,000$
* $1 \le K \le \frac{N(N-1)(N-2)}{6}$



Subtasks

Subtask 1 [ $160$ points ]


* $N \le 100$

Subtask 2 [ $240$ points ]


* $N \le 1000$

Subtask 3 [ $450$ points ]


* $N \le 200,000$

Input

The input is given from Standard Input in the following format:


> $N \ K$

Examples

Input

4 3


Output

1.0000000000000


Input

6 9


Output

0.86602540378


Input

12 220


Output

1.29903810568

### Response

```cpp
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef int _loop_int;
#define REP(i,n) for(_loop_int i=0;i<(_loop_int)(n);++i)
#define FOR(i,a,b) for(_loop_int i=(_loop_int)(a);i<(_loop_int)(b);++i)
#define FORR(i,a,b) for(_loop_int i=(_loop_int)(b)-1;i>=(_loop_int)(a);--i)

#define DEBUG(x) cout<<#x<<": "<<x<<endl
#define DEBUG_VEC(v) cout<<#v<<":";REP(i,v.size())cout<<" "<<v[i];cout<<endl
#define ALL(a) (a).begin(),(a).end()

#define CHMIN(a,b) a=min((a),(b))
#define CHMAX(a,b) a=max((a),(b))

// mod
const ll MOD = 1000000007ll;
#define FIX(a) ((a)%MOD+MOD)%MOD

// floating
typedef double Real;
const Real EPS = 1e-11;
#define EQ0(x) (abs(x)<EPS)
#define EQ(a,b) (abs(a-b)<EPS)
typedef complex<Real> P;

Real cross(P a,P b){
  return imag(conj(a)*b);
}

Real sur(P a,P b,P c){
  b-=a; c-=a;
  return abs(cross(b,c))/2.0;
}

P ppp[252521];

// count triangle s.t. surface < s
ll calc(int n,Real s){
  Real u = 2.0*M_PI/(Real)n;
  ll ans = 0;
  int a = 0;
  P x = ppp[a];
  ll bai = n;
  if(n%3==0)bai/=3;
  FOR(b,1,n-1){
    P y = ppp[b];
    int low = b+1, high = n-1;
    int cnt = (high-low+1);
    // seisannkakkei guard
    if(n%3==0 && b==n/3){
      cnt--;
    }
    if(cnt%2==1){
      int cent = low + cnt/2;
      P z = ppp[cent];
      if(sur(x,y,z) < s){
        ans += cnt;
        continue;
      }
    }
    cnt /= 2;
    high = low + cnt - 1 + 1;
    low--;
    while(low+1<high){
      int mid = (low+high)/2;
      P z = ppp[mid];
      if(sur(x,y,z) < s){
        low = mid;
      }else{
        high = mid;
      }
    }
    ans += 2ll*(low-b);
  }
  // DEBUG(ans);
  ans /= 3;
  ans *= n;
  return ans;
}

int main(){
  int n;
  ll k;
  cin>>n>>k;
  if(n%3==0 && (ll)n*(n-1)*(n-2)/6 == k){
    puts("1.29903810568");
    return 0;
  }
  Real u = 2.0*M_PI/(Real)n;
  P po = exp(P(0,u));
  ppp[0] = P(1,0);
  REP(i,n)ppp[i+1] = ppp[i]*po;
  Real low = 0.0, high = 1.3;
  // DEBUG(calc(n,2.0));
  REP(_,40){
    Real mid = (low+high)/2.0;
    ll cnt = calc(n,mid);
    // DEBUG(mid);
    // DEBUG(cnt);
    if(cnt >= k){
      high = mid;
    }else{
      low = mid;
    }
  }
  printf("%.12lf\n",low);
  return 0;
}

```