#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < (int)(n); ++i)
#define all(x) x.begin(),x.end()
#define ln '\n'
const long double PI = acos(-1.0L);
const long long MOD = 1000000007LL;
// const long long MOD = 998244353LL;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true;} return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true;} return false; }
////////////////////////////////////////////////////////////////////////////////////////////////////////


using DD = double; // 精度が足りないときはlong double
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)

//点
struct Point {
    DD x, y;
    Point (DD x = 0, DD y = 0): x(x), y(y) {}

    Point& operator+=(const Point &p) { x += p.x; y += p.y; return *this;}
    Point operator+(const Point &p) const { return Point(*this) += p;}
    Point& operator-=(const Point &p) { x -= p.x; y -= p.y; return *this;}
    Point operator-(const Point &p) const { return Point(*this) -= p;}
    Point& operator*=(DD a) { x *= a; y *= a; return *this;}
    Point operator*(DD a) const { return Point(*this) *= a;}
    Point& operator/=(DD a) { x /= a; y /= a; return *this;}
    Point operator/(DD a) const { return Point(*this) /= a;}
    bool operator== (const Point &p) const { return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;}
    bool operator< (const Point &p) const {
        if (equals(x, p.x)) return y < p.y;
        return x < p.x;
    }
    friend istream& operator >>(istream& is, Point& p) { is >> p.x >> p.y; return is;}
    friend ostream& operator <<(ostream& os, const Point& p) { os << p.x << " " << p.y; return os;}
};

//ベクトル
typedef Point Vector;

inline DD norm(const Vector &a) { return a.x * a.x + a.y * a.y;}
inline DD abs(const Vector &a) { return sqrt(norm(a));}
inline DD dot(const Vector &a, const Vector &b) { return a.x * b.x + a.y * b.y;}
inline DD cross(const Vector &a, const Vector &b) { return a.x * b.y - a.y * b.x;}
inline Point rot(const Point &p, DD ang) { return Point(cos(ang) * p.x - sin(ang) * p.y, sin(ang) * p.x + cos(ang) * p.y);}
inline Point rot90(const Point &p) { return Point(-p.y, p.x);}

//線分
struct Segment {
    Point p1,p2;
    Segment() = default;
    Segment(Point p1, Point p2) : p1(p1),p2(p2) {}
};

//直線
typedef Segment Line;

// 円
struct Circle {
    Point c;
    DD r;
    Circle(Point c = Point(), DD r = 0): c(c), r(r) {}
};

//多角形
typedef vector<Point> Polygon;

//射影
Point project(const Segment &s, const Point &p) {
    Vector base = s.p2 - s.p1;
    DD r = dot(p - s.p1, base) / norm(base);
    return s.p1 + base * r;
}

//線対称
inline Point reflect(const Segment &s, const Point &p) {return p + (project(s,p) - p) * 2;}

int ccw(const Point &p0, const Point &p1, const Point &p2) {
    Vector a = p1 - p0;
    Vector b = p2 - p0;
    if (cross(a,b) > EPS) return 1; //p0,p1から見てp2は左側(反時計回り)
    if (cross(a,b) < -EPS) return -1; //p0,p1から見てp2は右側(時計回り)
    if (dot(a,b) < -EPS) return 2; //p2-p0-p1の順に一直線上
    if (norm(a) < norm(b)) return -2; //p0-p1-p2の順に一直線上
    return 0; //p0-p2-p1の順に一直線上
}

//線分p1,p2とp3,p4の交差判定
inline bool intersect(const Point &p1, const Point &p2, const Point &p3, const Point &p4) { return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 && ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);}
inline bool intersect(const Segment &s1, const Segment &s2) { return intersect(s1.p1, s1.p2, s2.p1, s2.p2);}

inline DD getDistanceLP(const Line &l, const Point &p) { return abs(cross(l.p2 - l.p1,p - l.p1) / abs(l.p2 - l.p1));}
DD getDistanceSP(const Segment &s, const Point &p) {
    if (dot(s.p2 - s.p1,p - s.p1) < 0.0) return abs(p - s.p1);
    if (dot(s.p1 - s.p2,p - s.p2) < 0.0) return abs(p - s.p2);
    return getDistanceLP(s, p);
}
DD getDistance(const Segment &s1, const Segment &s2) {
    if (intersect(s1, s2)) return (DD)0;
    return min({getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2), getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)});
}

//線分と線分の交点
Point getCrossPoint(const Segment &s1, const Segment &s2) {
    Vector base = s2.p2 - s2.p1;
    DD d1 = abs(cross(base, s1.p1 - s2.p1));
    DD d2 = abs(cross(base, s1.p2 - s2.p1));
    DD t = d1 / (d1 + d2);
    return s1.p1 + (s1.p2 - s1.p1) * t;
}

//円と直線の交差判定
inline bool intersect(const Circle &c, const Line &l) { return getDistanceLP(l, c.c) - c.r < EPS;}
//円と円の交差判定
inline bool intersect(const Circle &c1, const Circle &c2) { return abs(c1.c - c2.c) - (c1.r + c2.r) < EPS && fabs(c1.r - c2.r) - abs(c1.c - c2.c) < EPS;}

//円と線分の交点
pair<Point, Point> getCrossPoints(const Circle &c, const Line &l) {
    assert(intersect(c,l));
    Vector pr = project(l, c.c);
    Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
    DD base = sqrt(c.r * c.r - norm(pr - c.c));
    return make_pair(pr + e * base, pr - e * base);
}

inline DD arg(const Vector &p) { return atan2(p.y, p.x);}
inline Vector polar(DD a, DD r) { return Point(cos(r) * a, sin(r) * a);}

//円と円の交点
pair<Point, Point> getCrossPoints(const Circle &c1, const Circle &c2) {
    assert(intersect(c1, c2));
    DD d = abs(c1.c - c2.c);
    DD a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (DD(2) * c1.r * d));
    DD t = arg(c2.c - c1.c);
    return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

//多角形の面積
DD area(const Polygon &g) {
    const int N = g.size();
    DD ret = 0;
    for (int i = 0; i < N; ++i) {
        ret += cross(g[i],g[(i+1)%N]);
    }
    return fabs(ret)/2;
}

// 多角形-点の包含判定
int containment(const Polygon &g, const Point &p) {
    const int N = g.size();
    int cnt = 0;
    for (int i = 0; i < N; ++i) {
        if (norm(g[i] - p) < EPS || norm(g[(i+1)%N] - p) < EPS || ccw(g[i], g[(i+1)%N], p) == 0) {
            return 1; // pがgの辺上に存在する
        }
        Point I = Point(2e9 + p.x, 2e9 + 574677631 + p.y);
        if (ccw(I, p, g[i]) == 0 || ccw(I, p, g[(i+1)%N]) == 0) continue;
        if (intersect(I, p, g[i], g[(i+1)%N])) ++cnt;
    }
    if (cnt&1) return 2; // pがgに含まれる
    else return 0; // pがgに含まれない
}

//象限
int ort(const Point &a) {
    if (norm(a) < EPS) return 0;
    if (a.y > 0) return a.x > 0 ? 1 : 2;
    return a.x > 0 ? 4 : 3;
}

bool xsort(const Point &a, const Point &b) {
    if (equals(a.x, b.x)) return a.y < b.y;
    return a.x < b.x;
}

bool ysort(const Point &a, const Point &b) {
    if (equals(a.y, b.y)) return a.x < b.x;
    return a.y < b.y;
}

bool argsortcross(const Point &a, const Point &b) {
    int ao = ort(a), bo = ort(b);
    if (ao != bo) return ao < bo;
    return cross(a,b) > 0;
}

bool argsortatan2(const Point &a, const Point &b) {
    return atan2(a.y, a.x) < atan2(b.y, b.x);
}

//凸包
Polygon andrewScan(Polygon s) {
    Polygon u,l;
    const int N = s.size();
    if (N < 3) return s;
    sort(s.begin(), s.end(), xsort);
    u.emplace_back(s[0]);
    u.emplace_back(s[1]);
    l.emplace_back(s[N-1]);
    l.emplace_back(s[N-2]);
    
    for (int i = 2; i < s.size(); ++i) {
        // 凸包上の点も含めるなら ccw() == 1
        for (int n = u.size(); n >= 2 && ccw(u[n-2],u[n-1],s[i]) != -1; --n) {
            u.pop_back();
        }
        u.emplace_back(s[i]);
    }

    for (int i = N - 3; i >= 0; --i) {
        // 凸包上の点も含めるなら ccw() == 1
        for (int n = l.size(); n >= 2 && ccw(l[n-2], l[n-1], s[i]) != -1; --n) {
            l.pop_back();
        }
        l.emplace_back(s[i]);
    }

    reverse(l.begin(), l.end());
    for (int i = u.size() - 2; i >= 1; --i) l.emplace_back(u[i]);

    return l;
}

//最遠点対
DD farthestpointpair(const Polygon &g) {
    const int N = g.size();
    if (N == 2) return abs(g[1] - g[0]);
    int i = 0, j = 0;
    for (int k = 0; k < N; ++k) {
        if (g[k].y > g[i].y) i = k;
        if (g[k].y < g[j].y) j = k;
    }

    DD ret = 0;
    int si = i, sj = j;
    while (i != sj || j != si) {
        ret = max(ret, abs(g[i]-g[j]));
        if (cross(g[(i+1)%N] - g[i], g[(j+1)%N] - g[j]) < -EPS) {
            i = (i+1)%N;
        } else {
            j = (j+1)%N;
        }
    }

    return ret;
}

int main() {
    ios::sync_with_stdio(false); cin.tie(nullptr);
    int N,K; cin >> N >> K;
    Polygon P(N);
    vector<int> d(N);
    rep(i,N) cin >> P[i] >> d[i];

    double ng = 0;
    double ok = 1e9;
    rep(_,100) {
        double mid = (ok+ng)/2;
        vector<Circle> C(N);
        rep(i,N) C[i] = Circle(P[i],mid/d[i]);
        Polygon R;
        rep(i,N) R.emplace_back(P[i]);
        rep(i,N) {
            for (int j = i+1; j < N; j++) {
                if (intersect(C[i],C[j])) {
                    Point a,b;
                    tie(a,b) = getCrossPoints(C[i],C[j]);
                    R.emplace_back(a);
                    R.emplace_back(b);
                }
            }
        }
        int ggg = 0;
        for (auto i : R) {
            int cnt = 0;
            rep(j,N) {
                if (abs(i - C[j].c) < C[j].r + EPS) cnt++;
            }
            chmax(ggg,cnt);
        }
        if (ggg < K) ng = mid;
        else ok = mid;
    }

    cout << fixed << setprecision(10) << ok << ln;
}



Measured memory_bytes: 384