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 <algorithm>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <queue>

using namespace std;

struct Node {
  double lower_bound, x, y, r;

  Node(double lower_bound, double x, double y, double r) : lower_bound(lower_bound), x(x), y(y), r(r) {}

  bool operator>(const Node &node) const {
    return lower_bound > node.lower_bound;
  }
};

int n, k;
vector<int> x, y, c;

double distance(double px, double py) {
  vector<double> dis(n);
  for (int i = 0; i < n; ++i) {
    double dx = abs(px - x[i]), dy = abs(py - y[i]);
    dis[i] = c[i] * hypot(dx, dy);
  }
  nth_element(dis.begin(), dis.begin() + k - 1, dis.end());
  return dis[k - 1];
}

double distance_lb(double px, double py, double r) {
  vector<double> dis(n);
  for (int i = 0; i < n; ++i) {
    double dx = abs(px - x[i]), dy = abs(py - y[i]);
    if (dx <= r) {
      if (dy <= r) {
        dis[i] = 0;
      } else {
        dis[i] = c[i] * (dy - r);
      }
    } else {
      if (dy <= r) {
        dis[i] = c[i] * (dx - r);
      } else {
        dis[i] = c[i] * hypot(dx - r, dy - r);
      }
    }
  }
  nth_element(dis.begin(), dis.begin() + k - 1, dis.end());
  return dis[k - 1];
}

int main() {
  cin >> n >> k;
  x.resize(n);
  y.resize(n);
  c.resize(n);
  for (int i = 0; i < n; ++i) {
    cin >> x[i] >> y[i] >> c[i];
  }
  priority_queue<Node, vector<Node>, greater<Node>> que;
  double res = distance(0, 0);
  que.emplace(distance_lb(0, 0, 1000), 0, 0, 1000);
  while (!que.empty()) {
    auto node = que.top();
    que.pop();
    if (res < node.lower_bound) {
      break;
    }
    for (double dx : {-0.5, 0.5}) {
      for (double dy : {-0.5, 0.5}) {
        double nx = node.x + dx * node.r, ny = node.y + dy * node.r, nr = node.r / 2;
        double dis_lb = distance_lb(nx, ny, nr);
        if (res - dis_lb > 5e-7 * max(1.0, dis_lb)) {
          res = min(res, distance(nx, ny));
          que.emplace(dis_lb, nx, ny, nr);
        }
      }
    }
  }
  cout << fixed << setprecision(15) << res << endl;
}