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;

using Real = long double;
using Point = complex< Real >;
const Real EPS = 1e-12, PI = acos(-1.0L);

inline bool eq(Real a, Real b) { return fabs(b - a) < EPS; }

istream &operator>>(istream &is, Point &p) {
  Real a, b;
  is >> a >> b;
  p = Point(a, b);
  return is;
}


struct Circle {
  Point p;
  Real r;

  Circle() = default;

  Circle(Point p, Real r) : p(p), r(r) {}
};

using Points = vector< Point >;
using Circles = vector< Circle >;

int checker(Circle c1, Circle c2) {
  if(c1.r < c2.r) swap(c1, c2);
  Real d = abs(c1.p - c2.p);
  if(c1.r + c2.r < d) return 4;
  if(eq(c1.r + c2.r, d)) return 3;
  if(c1.r - c2.r < d) return 2;
  if(eq(c1.r - c2.r, d)) return 1;
  return 0;
}

bool intersect(Circle c1, Circle c2) {
    int tmp = checker(c1, c2);
    return 1 <= tmp and tmp <= 3;
}


pair< Point, Point > crosspoint(const Circle &c1, const Circle &c2) {
  Real d = abs(c1.p - c2.p);
  Real a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
  Real t = atan2(c2.p.imag() - c1.p.imag(), c2.p.real() - c1.p.real());
  Point p1 = c1.p + Point(cos(t + a) * c1.r, sin(t + a) * c1.r);
  Point p2 = c1.p + Point(cos(t - a) * c1.r, sin(t - a) * c1.r);
  return {p1, p2};
}

int N, K;
Points P;
vector<int> c;
vector<long double> r;
Circles C;
void input() {
    cin >> N >> K;
    P.resize(N);
    c.resize(N);
    C.resize(N);
    r.resize(N);
    for(int i = 0; i < N; i++) {
        cin >> P[i] >> c[i];
    }
}

void solve() {
    long double ok = 1e6;
    long double ng = 0.0;
    for(int timer = 0; timer <= 40; timer++) {
        bool clear = false;
        long double mid = (ok + ng) / 2;
        for(int i = 0; i < N; i++) {
            r[i] = mid / c[i];
            C[i] = Circle(P[i], r[i]);
        }
        Points Check;
        for(int i = 0; i < N; i++) {
            Check.push_back(P[i]);
            for(int j = i + 1; j < N; j++) {
                if(intersect(C[i], C[j])) {
                    auto tmp = crosspoint(C[i], C[j]);
                    Check.push_back(tmp.first);
                    Check.push_back(tmp.second);
                }
            }
        }
        for(auto p : Check) {
            int cnt = 0;
            for(int i = 0; i < N; i++) {
                if(abs(P[i] - p) <= r[i] + EPS)  cnt++;
            }
            if(cnt >= K) clear = true;
        }
        if(clear) ok = mid;
        else ng = mid;
    }
    cout << fixed << setprecision(20) << ok << endl;
}

int main() {
    input();
    solve();
    return 0;
}