#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <iostream>
#include <istream>
#include <iterator>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
#include <tuple>
#include <iomanip>
#include <climits>
#include <fstream>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;
//typedef pair<ll, ll> P;
#define rep(i, n) for(int i = 0; i < (n); i++)
#define revrep(i, n) for(int i = (n)-1; i >= 0; i--)
#define pb push_back
#define f first
#define s second
#define chmin(x, y) x = min(x, y);
#define chmax(x, y) x = max(x, y);

//const ll INFL = LLONG_MAX;//10^18 = 2^60
const ll INFL = 1LL<<60;
//const int INF = INT_MAX;
const int INF = 1 << 30;//10^9
//ll MOD = 1000000007;
ll MOD = 998244353;
double EPS = 1e-10;

vector<ll> dy = {0, 1, 0, -1, 1, 1, -1, -1, 0};
vector<ll> dx = {1, 0, -1, 0, 1, -1, 1, -1, 0};

void pres(double A){printf("%.12lf\n", A);}
void BinarySay(ll x, ll y = 60){rep(i, y) cout << (x>>(y-1-i) & 1); cout << endl;}
ll cnt_bit(ll x){return __builtin_popcountll(x);}

ll pow_long(ll x, ll k){
  ll res = 1;
  while(k > 0){
    if(k % 2) res *= x;
    x *= x; k /= 2;
  }
  return res;
}

ll pow_mod(ll x, ll k){
  x %= MOD;
  ll res = 1;
  while(k > 0){
    if(k % 2){
      res *= x; res %= MOD;
    }
    x *= x; x %= MOD;
    k /= 2;
  }
  return res;
}

ll inverse(ll x){return pow_mod(x, MOD - 2);};

ll gcd(ll a, ll b){
    if(b == 0) return a;
    return gcd(b, a % b);
}

ll lcm(ll x, ll y){
  ll res = x / gcd(x, y);
  res *= y;
  return res;
};


//コンビネーション
const int MAXcomb = 2000010;
ll fac[MAXcomb], finv[MAXcomb], inv[MAXcomb];
//facはn!,finvは1/n!
//invは逆元
void COMinit(){
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for(int i = 2; i < MAXcomb; i++){
        fac[i] = fac[i-1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD/i) % MOD;
        finv[i] = finv[i-1] * inv[i] % MOD;
    }
}
ll comb(int n, int k){
    if(n < k) return 0;
    if(n < 0 || k < 0) return 0;
    return fac[n] * finv[k] % MOD * finv[n-k] % MOD;
}

const int MAXkai = 200010;
ll kai_memo[MAXkai];
ll kai(ll N){
  if(kai_memo[N] != 0) return kai_memo[N];
  if(N <= 1) return 1;
  return kai_memo[N] = N * kai(N-1) % MOD;
}

ll disit(ll s, ll base = 10){
  ll res = 0;
  while(s){
    res++;
    s /= base;
  }
  return res;
}

//約数の列挙O(√n)
vector<ll> divisor(ll n){
    vector<ll> res(0);
    for(ll i = 1; i * i <= n; i++){
        if(n % i == 0){
            res.push_back(i);
            if(i != n/i) res.push_back(n/i);
        }
    }
    sort(res.begin(), res.end());
    return res;
}

double dist(double y1, double x1, double y2, double x2){
  return sqrt(pow(y1 - y2, 2.0) + pow(x1 - x2, 2.0));
}

bool exist_Intersection(double y1, double x1, double r1, double y2, double x2, double r2){
  double d = dist(y1, x1, y2, x2);
  return max(r1, r2) - min(r1, r2) <= d && d <= r1 + r2;
}
pair<pair<double, double>, pair<double, double>> Intersection(double y1, double x1, double r1, double y2, double x2, double r2){
  if(!exist_Intersection(y1, x1, r1, y2, x2, r2)) return {{INFL, INFL}, {INFL, INFL}};
  y1 -= y2, x1 -= x2;//y2, x2を(0, 0)へ移動
  double y1_ = y1 * y1, x1_ = x1 * x1;
  double a = (x1_ + y1_ + r2*r2 - r1*r1) / 2.0;
  double y3, x3, y4, x4;
  double sq = sqrt((x1_+y1_)*r2*r2-a*a);
  y3 = (a * y1 - x1 * sq) / (x1_+y1_);
  y4 = (a * y1 + x1 * sq) / (x1_+y1_);
  x3 = (a * x1 + y1 * sq) / (x1_+y1_);
  x4 = (a * x1 - y1 * sq) / (x1_+y1_);
  return {{y3+y2, x3+x2}, {y4+y2, x4+x2}};
}

ll N, K;
double x[60], y[60], c[60];

void solve(){
  cin >> N >> K;
  rep(i, N) cin >> x[i] >> y[i] >> c[i];
  if(N == 1){
    cout << 0 << endl;
    return;
  }
  double ng = 0, ok = INFL;
  rep(_, 300){
    double mid = (ng + ok) / 2;
    vector<pair<double, double>> xs;
    rep(i, N) xs.pb({y[i], x[i]});
    rep(i, N)rep(j, N)if(i < j){
      double r1 = mid / c[i], r2 = mid / c[j];
      if(exist_Intersection(y[i], x[i], r1, y[j], x[j], r2)){
        pair<pair<double, double>, pair<double, double>> p = Intersection(y[i], x[i], r1, y[j], x[j], r2);
        xs.pb(p.f);
        xs.pb(p.s);
      }
    }
    bool can = 0;
    rep(i, xs.size()){
      int cnt = 0;
      rep(j, N){
        if(dist(xs[i].f, xs[i].s, y[j], x[j]) <= mid / c[j] + EPS) cnt++;
      }
      if(cnt >= K) can = 1;
    }
    if(can) ok = mid;
    else ng = mid;
  }
  pres(ok);
}


int main(){
  ios_base::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  solve();
}


Measured memory_bytes: 384