Problem: Takahashi wants to grill N pieces of meat on a grilling net, which can be seen as a two-dimensional plane. The coordinates of the i-th piece of meat are \left(x_i, y_i\right), and its hardness is c_i.

Takahashi can use one heat source to grill the meat. If he puts the heat source at coordinates \left(X, Y\right), where X and Y are real numbers, the i-th piece of meat will be ready to eat in c_i \times \sqrt{\left(X - x_i\right)^2 + \left(Y-y_i\right)^2} seconds.

Takahashi wants to eat K pieces of meat. Find the time required to have K or more pieces of meat ready if he put the heat source to minimize this time.

Constraints

* All values in input are integers.
* 1 \leq N \leq 60
* 1 \leq K \leq N
* -1000 \leq x_i , y_i \leq 1000
* \left(x_i, y_i\right) \neq \left(x_j, y_j\right) \left(i \neq j \right)
* 1 \leq c_i \leq 100

Input

Input is given from Standard Input in the following format:


N K
x_1 y_1 c_1
\vdots
x_N y_N c_N


Output

Print the answer.

It will be considered correct if its absolute or relative error from our answer is at most 10^{-6}.

Examples

Input

4 3
-1 0 3
0 0 3
1 0 2
1 1 40


Output

2.4


Input

10 5
-879 981 26
890 -406 81
512 859 97
362 -955 25
128 553 17
-885 763 2
449 310 57
-656 -204 11
-270 76 40
184 170 16


Output

7411.2252

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
/*#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>*/
 
#define pll              pair <long double,long double>
#define pb               push_back
#define ll               long double
#define ff               first
#define ss               second
#define D(x)             cerr<<#x " = "<<(x)<<endl
#define vll              vector <ll>
#define IOS              ios_base::sync_with_stdio(0); cin.tie(NULL);
#define endl             '\n'   
using namespace std;
using Real=double;
using Point=complex<Real>;
const Real EPS=1e-10;
const int N=60+1;
Point x[N];
Real c[N];
int n,k;

inline bool eq(Real a,Real b){
    return fabs(a-b)<EPS;
}

Real dis(Point a,Point b){
    return abs(a-b);
} 

struct Circle{
    Point center;
    Real r;
    Circle(Point center,Real r):center(center),r(r){}
};

bool intersect(Circle c,Point p){
    return abs(abs(p-c.center)-c.r)<EPS;
}

int intersect(Circle c1,Circle c2){
    if(c1.r<c2.r) swap(c1,c2);
    Real d=abs(c1.center-c2.center);
    if(c1.r+c2.r<d)     return 4;
    if(eq(c1.r+c2.r,d)) return 3;
    if(c1.r-c2.r<d)     return 2;
    if(eq(c1.r-c2.r,d)) return 1;
                        return 0;
}


vector<Point> crosspoint(Circle c1,Circle c2){
    vector<Point> ret;
    int isec=intersect(c1,c2);
    if(isec==0 or isec==4) return ret;
    Real d=abs(c1.center-c2.center);
    Real a=acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d));
    Real t=atan2(c2.center.imag()-c1.center.imag(),c2.center.real()-c1.center.real());
    ret.push_back(c1.center+Point(cos(t+a)*c1.r,sin(t+a)*c1.r));
    ret.push_back(c1.center+Point(cos(t-a)*c1.r,sin(t-a)*c1.r));
    return ret;
}


bool solve(Real tme)
{
	vector<Point>v;
	for(int i=0;i<n;i++)
	{
		v.push_back(x[i]);
	}
	for(int i=0;i<n;i++)
	{
		for(int j=i+1;j<n;j++)
		{
			vector<Point> inter = crosspoint(Circle(x[i],tme/c[i]),Circle(x[j],tme/c[j]));
			for(Point xx:inter)
			{
				v.push_back(xx);
			}
		}
	}
	//cerr<<v.size()<<endl;
	for(Point xx:v)
	{
		int f=0;
		for(int i=0;i<n;i++)
		{
			Real r = tme/c[i];
			if(abs(x[i]-xx)<r+EPS) f++;
		}
		//cout<<f<<endl;
		if(f>=k)
		{
			return true;
		}
	}
	return false;
}

int main()
{
    IOS
    cout<<fixed<<setprecision(12);
 	// freopen("input.txt","r",stdin);
 	// freopen("output.txt","w",stdout);
 	// freopen("error.txt","w",stderr);
	cin>>n>>k; 		
	for(int i=0;i<n;i++)
	{
		Real a,b;
		cin>>a>>b;
		x[i]=Point(a,b);
		cin>>c[i];
	}
	Real l=0,r=1000000000;
	int itr=0;
	for(int itr=0;itr<=100;itr++)
	{
		Real mid=(l+r)/2;
		bool ver=solve(mid);
		//cout<<mid<<" "<<ver<<endl;
		if(ver)
		{
			r=mid;
		}
		else
		{
			l=mid;
		}
	}
	cout<<l<<endl;
    return 0;
}