#include <algorithm>
#include <bitset>
#include <cmath>
#include <complex>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <regex>
#include <set>
#include <stack>
#include <string>
#include <vector>

const int MOD = 1e9 + 7;
const int iINF = 2147483647 / 2;
const long long int llINF = 9223372036854775807 / 2;

using namespace std;
using ld = long double;
using ll = long long int;
using vl = vector<ll>;
using vvl = vector<vector<ll>>;
using vvvl = vector<vector<vector<ll>>>;

typedef pair<ll, ll> pll;
bool paircomp(const pll &a, const pll &b) {
  if (a.first == b.first)
    return a.second < b.second;
  return a.first < b.first;
}

#define REP(i, n) for (ll i = 0; i < (n); i++)
#define RREP(i, n) for (ll i = (n)-1; i >= 0; i--)
#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define AUTO(i, m) for (auto &i : m)
#define ALL(a) (a).begin(), (a).end()
#define MAX(vec) *std::max_element(vec.begin(), vec.end())
#define MIN(vec) *std::min_element(vec.begin(), vec.end())
#define ARGMAX(vec)                                                            \
  std::distance(vec.begin(), std::max_element(vec.begin(), vec.end()))
#define ARGMIN(vec)                                                            \
  std::distance(vec.begin(), std::min_element(vec.begin(), vec.end()))
#define REV(T) greater<T>()
#define PQ(T) priority_queue<T, vector<T>, greater<T>>
#define VVL(a, b, c) vector<vector<ll>>(a, vector<ll>(b, c))
#define VV(T, a, b, c) vector<vector<T>>(a, vector<T>(b, c))
#define VVVL(a, b, c, d)                                                       \
  vector<vector<vector<ll>>>(a, vector<vector<ll>>(b, vector<ll>(c, d)))
#define VVV(T, a, b, c, d)                                                     \
  vector<vector<vector<T>>>(a, vector<vector<T>>(b, vector<T>(c, d)))
#define SP(a) setprecision(a)
#define SQRT(a) sqrt((long double)(a))
#define DPOW(a, b) pow((long double)(a), (long double)(b))
#define UNIQUE(vec)                                                            \
  do {                                                                         \
    sort(ALL((vec)));                                                          \
    (vec).erase(std::unique(ALL((vec))), (vec).end());                         \
  } while (0)

ll POW(ll n, ll m) {
  if (m == 0) {
    return 1;
  } else if (m % 2 == 0) {
    ll tmp = POW(n, m / 2);
    return (tmp * tmp);
  } else {
    return (n * POW(n, m - 1));
  }
}

int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

typedef long double D; // 座標値の型。doubleかlong doubleを想定
typedef complex<D> P;  // Point
typedef pair<P, P> L;  // Line
typedef vector<P> VP;
const D EPS = 1e-9; // 許容誤差。問題によって変える
#define X real()
#define Y imag()
#define LE(n, m) ((n) < (m) + EPS)
#define GE(n, m) ((n) + EPS > (m))
#define EQ(n, m) (abs((n) - (m)) < EPS)

// 2円の交点
VP crosspointCC(P a, D ar, P b, D br) {
  VP ps;
  P ab = b - a;
  D d = abs(ab);
  D crL = (norm(ab) + ar * ar - br * br) / (2 * d);
  if (EQ(d, 0) || ar < abs(crL))
    return ps;

  P abN = ab * P(0, sqrt(ar * ar - crL * crL) / d);
  P cp = a + crL / d * ab;
  ps.push_back(cp + abN);
  if (!EQ(norm(abN), 0))
    ps.push_back(cp - abN);
  return ps;
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ll N, K;
  cin >> N >> K;
  vector<ld> x(N), y(N), c(N);
  REP(i, N) cin >> x[i] >> y[i] >> c[i];

  ld left = 0;
  ld right = 1e20;

  while (abs(right - left) > EPS) {
    ld mid = left + (right - left) / 2;
    // cout << mid << endl;
    vector<ld> c2(N);
    REP(i, N) c2[i] = mid / c[i];
    VP po;
    REP(i, N) po.push_back(P(x[i], y[i]));
    REP(i, N - 1) FOR(j, i + 1, N) {
      AUTO(cr, crosspointCC(P(x[i], y[i]), c2[i], P(x[j], y[j]), c2[j])) {
        po.push_back(cr);
      }
    }
    ll score = 0;
    AUTO(cr, po) {
      ll count = 0;
      REP(i, N) {
        if (norm(cr - P(x[i], y[i])) <= c2[i] * c2[i] + EPS)
          count++;
        score = max(score, count);
      }
    }

    if (score >= K)
      right = mid;
    else
      left = mid;
  }
  cout << SP(20) << right << endl;

  return 0;
}


Measured memory_bytes: 384