#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
const int maxn=67;
const int inf=INT_MAX;
const ll inff=1e18;
const ll mod=1e9+7;
#define pii pair<int,int>
#define mkp make_pair
#define F first
#define S second
#define pb push_back
#define sz(v) ((int)(v).size())
#define all(v) (v).begin(),(v).end()
//#define int ll

#ifdef HNO2
#define IOS
#else
#define endl '\n'
#define IOS ios::sync_with_stdio(0); cin.tie(0);
#endif // HNO2

int n,k;
int x[maxn],y[maxn],c[maxn];
long double r[maxn];

const long double eps=(1e-10);

int check2(long double X,long double Y)
{
    int cnt=0;
    for (int i=1;i<=n;i++)
        cnt+=(hypot(X-x[i],Y-y[i])<=r[i]+eps);
    return cnt>=k;
}

void get_intersection(int X,int Y,vector<pair<long double,long double> > &v)
{
    long double dist=hypot(x[X]-x[Y],y[X]-y[Y]);
    if (dist>r[X]+r[Y]||dist<abs(r[X]-r[Y])) return;

    long double costheta=(r[X]*r[X]+dist*dist-r[Y]*r[Y])/(2*r[X]*dist);
    long double sintheta=sqrt(1.0-costheta*costheta);

    long double xx=(x[Y]-x[X])*(r[X]/dist),yy=(y[Y]-y[X])*(r[X]/dist);

    v.pb(mkp(x[X]+xx*costheta-yy*sintheta,y[X]+xx*sintheta+yy*costheta));
    v.pb(mkp(x[X]+xx*costheta+yy*sintheta,y[X]+xx*sintheta-yy*costheta));
}

bool check(long double X)
{
    for (int i=1;i<=n;i++) r[i]=X/c[i];

    vector<pair<long double,long double> > v;

    int ok=0;
    for (int i=1;i<=n;i++) ok=max(ok,check2(x[i],y[i]));
    for (int i=1;i<=n;i++)
        for (int j=i+1;j<=n;j++)
    {
        v.clear();
        get_intersection(i,j,v);
        for (auto l:v) ok=max(ok,check2(l.F,l.S));
    }
    return ok;
}

int32_t main()
{
    IOS
    cin>>n>>k;
    for (int i=1;i<=n;i++) cin>>x[i]>>y[i]>>c[i];

    long double L=0.0,R=500000.0;
    for (int _=1;_<=80;_++)
    {
        long double M=(L+R)/2;
        if (check(M)) R=M;
        else L=M;
    }
    cout<<fixed<<setprecision(15)<<R<<endl;
}

