#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <map>
#include <cmath>
#include <queue>
#include <deque>
#include <set>
#include <iomanip>
#include <utility>
typedef long long ll;
typedef long double ld;
using namespace std;

ld x[70], y[70], c[70];
ld r[70], d[70][70], ang[70][70];
ld pi=abs(acos(-1.0));

ld dist(ld x1, ld y1, ld x2, ld y2){
	return pow((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2), 0.5);
}

ld yogen(ld a, ld b, ld c){
	return acos((a*a+b*b-c*c)/(a*b*2.0));
}

int main() {
	int N, K;
	cin >> N >> K;
	for(int i=0; i<N; ++i){
		cin >> x[i] >> y[i] >> c[i];
	}
	for(int i=0; i<N; ++i){
		for(int j=0; j<N; ++j){
			d[i][j]=dist(x[i], y[i], x[j], y[j]);
			ang[i][j]=atan2(y[j]-y[i], x[j]-x[i]);
		}
	}
	ld ng=0.0, ok=1e9, er=1e-10;
	while(ng+er<ok){
		ld mid=(ng+ok)/2.0;
		for(int i=0; i<N; ++i) r[i]=mid/c[i];
		int mx=0;
		for(int i=0; i<N; ++i){
			vector<pair<ld, int>> v;
			int stt=1;
			for(int j=0; j<N; ++j){
				if(i!=j){
					if(d[i][j]+r[i]<=r[j]+er) ++stt;
					else if(d[i][j]+er<r[i]+r[j]){
						ld p=yogen(r[i], d[i][j], r[j]);
						if(ang[i][j]-p<(-pi)){
							++stt;
							v.emplace_back(make_pair(ang[i][j]-p+pi*2.0, 1));
						}else{
							v.emplace_back(make_pair(ang[i][j]-p, 1));
						}
						if(ang[i][j]+p>pi){
							++stt;
							v.emplace_back(make_pair(ang[i][j]+p-pi*2.0, -1));
						}else{
							v.emplace_back(make_pair(ang[i][j]+p, -1));
						}
					}
				}
			}
			sort(v.begin(), v.end());
			mx=max(mx, stt);
			for(int i=0; i<v.size(); ++i){
				stt += v[i].second;
				mx=max(mx, stt);
			}
		}
		if(mx>=K) ok=mid;
		else ng=mid;
	}
	cout << setprecision(15) << ok << endl;
	return 0;
}