Problem: Takahashi wants to grill N pieces of meat on a grilling net, which can be seen as a two-dimensional plane. The coordinates of the i-th piece of meat are \left(x_i, y_i\right), and its hardness is c_i.

Takahashi can use one heat source to grill the meat. If he puts the heat source at coordinates \left(X, Y\right), where X and Y are real numbers, the i-th piece of meat will be ready to eat in c_i \times \sqrt{\left(X - x_i\right)^2 + \left(Y-y_i\right)^2} seconds.

Takahashi wants to eat K pieces of meat. Find the time required to have K or more pieces of meat ready if he put the heat source to minimize this time.

Constraints

* All values in input are integers.
* 1 \leq N \leq 60
* 1 \leq K \leq N
* -1000 \leq x_i , y_i \leq 1000
* \left(x_i, y_i\right) \neq \left(x_j, y_j\right) \left(i \neq j \right)
* 1 \leq c_i \leq 100

Input

Input is given from Standard Input in the following format:


N K
x_1 y_1 c_1
\vdots
x_N y_N c_N


Output

Print the answer.

It will be considered correct if its absolute or relative error from our answer is at most 10^{-6}.

Examples

Input

4 3
-1 0 3
0 0 3
1 0 2
1 1 40


Output

2.4


Input

10 5
-879 981 26
890 -406 81
512 859 97
362 -955 25
128 553 17
-885 763 2
449 310 57
-656 -204 11
-270 76 40
184 170 16


Output

7411.2252

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

struct Point {
  double x, y;
  
  Point() = default;
  Point(double x, double y) : x(x), y(y) {}

  Point operator+(const Point &p) const { return Point(x + p.x, y + p.y); }
  Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); }
  Point operator*(double d) const { return Point(x * d, y * d); }
  Point operator/(double d) const { return Point(x / d, y / d); }
  double operator*(const Point &p) const { return x * p.x + y * p.y; }
  double operator%(const Point &p) const { return x * p.y - y * p.x; }
};

double Dist(const Point &a, const Point &b) {
  return sqrt((a - b) * (a - b));
}

Point Rotate(const Point &a, double ang) {
  return Point(a.x * cos(ang) - a.y * sin(ang), a.x * sin(ang) + a.y * cos(ang));
}

int main() {
  int n, k;
  cin >> n >> k;
  vector<int> x(n), y(n), c(n);
  for (int i = 0; i < n; ++i) cin >> x[i] >> y[i] >> c[i];

  vector<Point> p(n);
  for (int i = 0; i < n; ++i) p[i] = Point(x[i], y[i]);

  double l = 0.0, r = 1e9;
  constexpr int kIter = 200;
  constexpr double kEps = 1e-6;

  for (int it = 0; it < kIter; ++it) {
    double mid = 0.5 * (l + r);
    vector<double> rad(n);
    // mid = 2.40000000;
    for (int i = 0; i < n; ++i) {
      rad[i] = mid / c[i];
      // cout << "rad[" << i << "] = " << rad[i] << endl;
    }
    vector<Point> ints(p.begin(), p.end());
    for (int i = 0; i < n; ++i) {
      for (int j = i + 1; j < n; ++j) {
        double dist = Dist(p[i], p[j]);
        if (dist > rad[i] + rad[j]) continue;
        if (dist < fabs(rad[i] - rad[j])) continue;
        Point vec = p[i] - p[j];
        double ang = acos((rad[j] * rad[j] + dist * dist - rad[i] * rad[i]) / (2 * rad[j] * dist));
        Point v1 = Rotate(vec, ang);
        Point v2 = Rotate(vec, -ang);
        v1 = v1 / sqrt(v1 * v1) * rad[j];
        v2 = v2 / sqrt(v2 * v2) * rad[j];
        // assert(fabs(Dist(p[j] + v1, p[j]) - rad[j]) < kEps);
        // assert(fabs(Dist(p[j] + v2, p[j]) - rad[j]) < kEps);
        // assert(fabs(Dist(p[j] + v1, p[i]) - rad[i]) < kEps);
        // assert(fabs(Dist(p[j] + v2, p[i]) - rad[i]) < kEps);
        ints.push_back(p[j] + v1);
        ints.push_back(p[j] + v2);
        // cout << "ints: " << (p[j] + v1).x << " " << (p[j] + v1).y << endl;
        // cout << "ints: " << (p[j] + v2).x << " " << (p[j] + v2).y << endl;
      }
    }
    bool ok = false;
    for (const auto &e : ints) {
      int cnt = 0;
      for (int i = 0; i < n; ++i) cnt += Dist(e, p[i]) < rad[i] + kEps;
      ok |= cnt >= k;
    }
    // cout << "ok = " << ok << endl;
    // exit(0);
    (ok ? r : l) = mid;
  }
  cout << fixed << setprecision(20) << l << "\n";
  return 0;
}