#include <bits/stdc++.h>
#ifdef LOCAL_DEBUG
#define DEBUG 1
#define CERR if(DEBUG) cerr
#define MACRO(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10,NAME,...) NAME
#define pr(...) CERR<<MACRO(__VA_ARGS__,pr10,pr9,pr8,pr7,pr6,pr5,pr4,pr3,pr2,pr1)(__VA_ARGS__)<<endl
#define pr1(a) (#a)<<"="<<(a)<<" "
#define pr2(a,b) pr1(a)<<pr1(b)
#define pr3(a,b,c) pr1(a)<<pr2(b,c)
#define pr4(a,b,c,d) pr1(a)<<pr3(b,c,d)
#define pr5(a,b,c,d,e) pr1(a)<<pr4(b,c,d,e)
#define pr6(a,b,c,d,e,f) pr1(a)<<pr5(b,c,d,e,f)
#define pr7(a,b,c,d,e,f,g) pr1(a)<<pr6(b,c,d,e,f,g)
#define pr8(a,b,c,d,e,f,g,h) pr1(a)<<pr7(b,c,d,e,f,g,h)
#define pr9(a,b,c,d,e,f,g,h,i) pr1(a)<<pr8(b,c,d,e,f,g,h,i)
#define pr10(a,b,c,d,e,f,g,h,i,j) pr1(a)<<pr9(b,c,d,e,f,g,h,i,j)
#define prArr(a){CERR<<(#a)<<"={";int i=0;for(auto t:(a))CERR<<(i++?", ":"")<<t;CERR<<"}"<<endl;}
#else
#define DEBUG 0
#define pr(...)
#define prArr(a)
#endif
using namespace std;
using Int = long long;
using _int = int;
using ll = long long;
using Double = long double;
const Int INF = (1LL<<60)+1e9; // ~ 1.15 * 1e18
const Int mod = (1e9)+7;
const Double EPS = 1e-8;
const Double PI = 6.0 * asin((Double)0.5);
//using P = pair<Int,Int>;
template<class T> T Max(T &a,T b){return a=max(a,b);}
template<class T> T Min(T &a,T b){return a=min(a,b);}
template<class T1, class T2> ostream& operator<<(ostream& o,pair<T1,T2> p){return o<<"("<<p.first<<","<<p.second<<")";}
template<class T1, class T2, class T3> ostream& operator<<(ostream& o,tuple<T1,T2,T3> t){return o<<"("<<get<0>(t)<<","<<get<1>(t)<<","<<get<2>(t)<<")";}
template<class T1, class T2> istream& operator>>(istream& i,pair<T1,T2> &p){return i>>p.first>>p.second;}
template<class T> ostream& operator<<(ostream& o,vector<T> a){Int i=0;for(T t:a)o<<(i++?" ":"")<<t;return o;}
template<class T> istream& operator>>(istream& i,vector<T> &a){for(T &t:a)i>>t;return i;}
//INSERT ABOVE HERE


using P = complex<Double>;
using C = pair<P, Double>;
Int check(C t1, C t2){
  P a, b;
  Double r1, r2;
  tie(a, r1) = t1;
  tie(b, r2) = t2;
  Double dis = abs(a - b);
  if(dis + EPS > r1 + r2) return 0;
  if(dis < r1 || dis < r2) return 0;
  if(abs(dis - (r1 + r2)) < EPS) return 1;
  return 2;
}

vector<P> get(C t1, C t2){
  P a, b;
  Double r1, r2;
  tie(a, r1) = t1;
  tie(b, r2) = t2;
  if(check(t1, t2) == 0) return {};
  if(check(t1, t2) == 1) return {(b - a)/abs(b - a) * r1 + a};
  Double l = abs(b - a);
  Double cos_ = (r2 * r2 - (r1 * r1 + l * l)) / (-2 * l * r1);
  Double sin_ = sin(acos(cos_));
  assert(!isnan(sin_));
  P res1 = (b - a) / abs(b - a) * r1 * P(cos_, sin_) + a;
  P res2 = (b - a) / abs(b - a) * r1 * P(cos_, -sin_) + a;
  return {res1, res2};
}

signed main(){
  srand((unsigned)time(NULL));
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);

  Int N, K;
  cin>>N>>K;
  vector<C> A(N);
  for(Int i=0;i<N;i++){
    Int a, b, c;
    cin>>a>>b>>c;
    A[i] = C(P(a, b), c);
  }

  auto check = [&](Double X){
    vector<C> B(N);
    for(Int i=0;i<N;i++) B[i] = C(A[i].first, X / A[i].second);

    auto check2=[&](P c){
      Int k = 0;
      for(Int i=0;i<N;i++) k += abs(c - B[i].first) <= B[i].second + EPS;
      return k >= K;
    };

    for(Int i=0;i<N;i++)
      for(Int j=i+1;j<N;j++){
        auto g = get(B[i], B[j]);
        for(auto c:g) if(check2(c)) return 1;
      }
    for(Int i=0;i<N;i++)
      if(check2(B[i].first)) return 1;
    return 0;
  };

  Double L = 0, R = INF;
  for(Int i=0;i<200;i++){
    Double M = (L + R) / 2;
    check(M)? (R = M):(L = M);
  }

  cout<<L<<endl;

  return 0;
}


Measured memory_bytes: 256