#include <bits/stdc++.h>
using namespace std;
#define BIT(n) (1LL << (n))
#define BITF(n, i) (((n) >> (i)) & 1)
#define REP(i, n) for (int i = 0; i < n; i++)
#define FOR(i, m, n) for (int i = m; i < n; i++)
#define REPI(i, x) for (int i = 1; i <= x; i++)
#define FORI(i, m, n) for (int i = m; i <= n; i++)
#define REPR(i, n) for (int i = n; i >= 0; i--)
#define REPZ(i, x) for (int i = 0; i <= x; i++)
#define FORA(i, n) for (auto &&i : n)
#define POW(a, b) ((int)(pow(a, b) + .5))
#define MODULO(a, b) (((a) % (b)) < 0 ? (a) % (b) + (b) : (a) % (b))
#define DUMPOUT cerr
// vector
template <typename T> istream &operator>>(istream &is, vector<T> &vec) {
  for (T &x : vec) is >> x;
  return is;
}
// pair
template <typename T, typename U> ostream &operator<<(ostream &os, pair<T, U> &pair_var) {
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}
// vector
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  os << "{";
  REP(i, (int)vec.size())
  os << vec[i] << (i + 1 == (int)vec.size() ? "" : ", ");
  os << "}";
  return os;
}
// map
template <typename T, typename U> ostream &operator<<(ostream &os, map<T, U> &map_var) {
  os << "{";
  FORA(itr, map_var) {
    os << *itr;
    itr++;
    if (itr != map_var.end()) os << ", ";
    itr--;
  }
  os << "}";
  return os;
}
// set
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) {
  os << "{";
  FORA(itr, set_var) {
    os << *itr;
    itr++;
    if (itr != set_var.end()) os << ", ";
    itr--;
  }
  os << "}";
  return os;
}
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) {
  DUMPOUT << head;
  if (sizeof...(Tail) > 0) DUMPOUT << ", ";
  dump_func(std::move(tail)...);
}
#ifdef DEBUG_
#define DEB
#define DUMP(...)                                                             \
  DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                             \
          << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \
          << "    ",                                                          \
      dump_func(__VA_ARGS__)
#define PRINTARR(x, y)                                     \
  cerr << #x << "=\n";                                     \
  for (auto itr = x; itr != y; itr++) cerr << *itr << " "; \
  cerr << endl;
#define PRINTARR2(x, i0, i1)                                       \
  cerr << #x << "=\n";                                             \
  for (int ii0 = 0; ii0 < i0; ii0++) {                             \
    for (int ii1 = 0; ii1 < i1; ii1++) cerr << x[ii0][ii1] << " "; \
    cerr << endl;                                                  \
  }
#else
#define DEB if (false)
#define DUMP(...)
#define PRINTARR(x, y)
#define PRINTARR2(x, i0, i1)
#endif
#define ALL(v) v.begin(), v.end()
#define fst first
#define snd second
#define mp make_pair
#define pb push_back
#define epb emplace_back
#define int long long
#define pint pair<int, int>
#define double long double
using namespace std;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> using vec = std::vector<T>;
template <class T> void print(const T &x) { cout << x << "\n"; }
const int MOD = 1000000007, INF0 = 1061109567, INF = INF0 * INF0;
const double EPS = 1e-8, PI = acos(-1.0);
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
/*
[&] { return; }();下のスラッシュを2つ追加しただけ.上のスラッシュを2つにすれば外れる.
//*/
#define MAXN 70
int N, K;
int x[MAXN], y[MAXN], c[MAXN];
// a bには座標情報　最後の成分は半径　交点を求めるプログラムである
vec<pair<double, double>> getP(vec<double> a, vec<double> b) {
  double ra = a[2];
  double rb = b[2];
  double angle = atan2(b[1] - a[1], b[0] - a[0]);
  double dis = 0;
  REP(i, 2) dis += pow(b[i] - a[i], 2);
  dis = sqrt(dis);

  //三角が成り立つ公式
  if (dis > ra + rb || ra > dis + rb || rb > dis + ra || dis == 0) return vec<pair<double, double>>();
  vec<pair<double, double>> tmp;
  if (dis == ra + rb || dis == ra - rb) {
    tmp.resize(1);
    tmp[0].fst = a[0] + ra;
    tmp[0].snd = a[1];
  } else if (dis == rb - ra) {
    tmp.resize(1);
    tmp[0].fst = a[0] - ra;
    tmp[0].snd = a[1];
  } else {
    tmp.resize(2);
    double pa = dis / 2 + (ra * ra - rb * rb) / (2 * dis);
    double h = sqrt(ra * ra - pa * pa);
    tmp[0].fst = a[0] + pa;
    tmp[0].snd = a[1] + h;
    tmp[1].fst = a[0] + pa;
    tmp[1].snd = a[1] - h;
    DUMP(ra, pa, h, a[0], a[1], ra, b[0], b[1], rb);
  }
  FORA(e, tmp) {
    double retx = e.fst - a[0];
    double rety = e.snd - a[1];
    e.fst = a[0] + retx * cos(angle) - rety * sin(angle);
    e.snd = a[1] + retx * sin(angle) + rety * cos(angle);
    DUMP(e.fst, e.snd);
  }
  return tmp;
}
bool isOK(double val) {
  if (val < 0) return false;
  REP(i, N) {
    FOR(j, i + 1, N) {
      vec<double> a{(double)x[i], (double)y[i], (double)val / c[i]};
      vec<double> b{(double)x[j], (double)y[j], (double)val / c[j]};
      vec<pair<double, double>> p = getP(a, b);
      //   DUMP(p.size());
      FORA(e, p) {
        double posx = e.fst;
        double posy = e.snd;
        int cnt = 0;
        REP(k, N) {
          double ret = c[k] * sqrt(pow(x[k] - posx, 2) + pow(y[k] - posy, 2));
          cnt += ret - EPS <= val;
          if (k == i || k == j) DUMP(k, i, j, ret, val, cnt, ret <= val);
        }

        // assert(cnt >= 2);
        if (cnt >= K) return true;
      }
    }
  }
  REP(i, N) {
    double posx = x[i];
    double posy = y[i];
    int cnt = 0;
    REP(k, N) {
      double ret = c[k] * sqrt(pow(x[k] - posx, 2) + pow(y[k] - posy, 2));
      cnt += ret - EPS <= val;
    }
    if (cnt >= K) return true;
  }
  return false;
}
signed main() {
  cin.tie(0), ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);
  cerr << fixed << setprecision(6);
  cin >> N >> K;

  REP(i, N) cin >> x[i] >> y[i] >> c[i];
  double left = 0;          // false
  double right = 1e7 + 10;  // true
  while (abs(right - left) > EPS && abs((right - left) / right) > EPS) {
    double mid = (left + right) / 2;
    DUMP(isOK(mid), mid);
    if (isOK(mid)) {
      right = mid;
    } else {
      left = mid;
    }
  }
  print(right);
}

Measured memory_bytes: 384