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;
#define fs first
#define sc second
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ALL(A) A.begin(),A.end()
#define RALL(A) A.rbegin(),A.rend()
typedef long long LL;
typedef pair<LL,LL> P;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
template<typename T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
const LL mod=1000000007;
const LL LINF=1LL<<62;
const int INF=1<<30;
int dx[]={1,0,-1,0,1,-1,1,-1};
int dy[]={0,1,0,-1,1,-1,-1,1};

typedef long double Real;
typedef complex<Real> Point;
typedef pair<Point, Point> Line;
typedef pair<Point, Real> Circle;
typedef vector<Point> Poly;

Real eps = 1e-9;

vector<Point> CCintersect (Circle c, Circle d) {
    vector<Point> ret;
    const Real dist = abs(c.first - d.first);
    const Real cr = c.second;
    const Real dr = d.second;

    if (dist > cr + dr) return ret;
    if (dist < abs(cr - dr)) return ret;

    const Real s = (cr + dr + dist) / 2.;
    const Real area = sqrt(s * (s - cr) * (s - dr) * (s - dist));
    const Real h = 2 * area / dist;

    Point v = d.first - c.first; v /= abs(v);
    const Point m = c.first + sqrt(cr * cr - h * h) * v;
    const Point n = v * Point(0, 1);

    ret.push_back(m + n * h);
    ret.push_back(m - n * h);
    return ret;
}

int main(){
    int n,k;cin >> n >> k;
    vector<long double> x(n),y(n),c(n);
    for (int i = 0; i < n; i++) {
        cin >> x[i] >> y[i] >> c[i];
    }
    long double l = 0, r = 1e9;
    while(abs(r-l)>eps){
        long double m = (r + l) / 2;
        vector<Circle> v(n);
        for (int i = 0; i < n; i++) {
            v[i].fs = Point(x[i],y[i]);
            v[i].sc = m / c[i];
        }
        vector<Point> p;
        for (int i = 0; i < n; i++) {
            for (int j = i+1; j < n; j++) {
                auto q = CCintersect(v[i],v[j]);
                for (int k = 0; k < q.size(); k++) {
                    p.pb(q[k]);
                }
            }
            p.pb(v[i].fs);
        }
        bool f = false;
        for (int i = 0; i < p.size(); i++) {
            int cnt = 0;
            for (int j = 0; j < n; j++) {
                double r = abs(p[i] - v[j].fs);
                if(r <= v[j].sc + eps) cnt++;
            }
            if(cnt >= k) f = true;
        }
        if(f) r = m;
        else l = m;
    }
    cout << setprecision(30) << fixed << r << endl;
    return 0;
}