#include <bits/stdc++.h>
#define rep(i, n) for (lli i = 0; i < (n); i++)
#define rrep(i, n) for (lli i = (n)-1; i >= 0; i--)
using namespace std;

using lli = long long int;
void YESNO(bool), YesNo(bool);
template <class T1, class T2>
bool chmin(T1 &l, const T2 &r);
template <class T1, class T2>
bool chmax(T1 &l, const T2 &r);

// cite: https://beet-aizu.github.io/library/library/geometry/geometry.cpp.html

#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)
const double PI = asinl(1) * 2;

// COUNTER CLOCKWISE
static const int CCW_COUNTER_CLOCKWISE = 1;
static const int CCW_CLOCKWISE = -1;
static const int CCW_ONLINE_BACK = 2;
static const int CCW_ONLINE_FRONT = -2;
static const int CCW_ON_SEGMENT = 0;

// intercsect of circles
static const int ICC_SEPERATE = 4;
static const int ICC_CIRCUMSCRIBE = 3;
static const int ICC_INTERSECT = 2;
static const int ICC_INSCRIBE = 1;
static const int ICC_CONTAIN = 0;

struct Point
{
  double x, y;
  Point() {}
  Point(double x, double y) : x(x), y(y) {}
  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  Point operator*(double k) { return Point(x * k, y * k); }
  Point operator/(double k) { return Point(x / k, y / k); }
  double norm() { return x * x + y * y; }
  double abs() { return sqrt(norm()); }

  bool operator<(const Point &p) const
  {
    return x != p.x ? x < p.x : y < p.y;
    //grid-point only
    //return !equals(x,p.x)?x<p.x:!equals(y,p.y)?y<p.y:0;
  }

  bool operator==(const Point &p) const
  {
    return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
  }
};

struct EndPoint
{
  Point p;
  int seg, st;
  EndPoint() {}
  EndPoint(Point p, int seg, int st) : p(p), seg(seg), st(st) {}
  bool operator<(const EndPoint &ep) const
  {
    if (p.y == ep.p.y)
      return st < ep.st;
    return p.y < ep.p.y;
  }
};

istream &operator>>(istream &is, Point &p)
{
  is >> p.x >> p.y;
  return is;
}

ostream &operator<<(ostream &os, Point p)
{
  os << fixed << setprecision(12) << p.x << " " << p.y;
  return os;
}

bool sort_x(Point a, Point b)
{
  return a.x != b.x ? a.x < b.x : a.y < b.y;
}

bool sort_y(Point a, Point b)
{
  return a.y != b.y ? a.y < b.y : a.x < b.x;
}

typedef Point Vector;
typedef vector<Point> Polygon;

istream &operator>>(istream &is, Polygon &p)
{
  for (int i = 0; i < (int)p.size(); i++)
    is >> p[i];
  return is;
}

struct Segment
{
  Point p1, p2;
  Segment() {}
  Segment(Point p1, Point p2) : p1(p1), p2(p2) {}
};
typedef Segment Line;

istream &operator>>(istream &is, Segment &s)
{
  is >> s.p1 >> s.p2;
  return is;
}

struct Circle
{
  Point c;
  double r;
  Circle() {}
  Circle(Point c, double r) : c(c), r(r) {}
};

istream &operator>>(istream &is, Circle &c)
{
  is >> c.c >> c.r;
  return is;
}

double norm(Vector a)
{
  return a.x * a.x + a.y * a.y;
}
double abs(Vector a)
{
  return sqrt(norm(a));
}
double dot(Vector a, Vector b)
{
  return a.x * b.x + a.y * b.y;
}
double cross(Vector a, Vector b)
{
  return a.x * b.y - a.y * b.x;
}

Point orth(Point p) { return Point(-p.y, p.x); }

bool isOrthogonal(Vector a, Vector b)
{
  return equals(dot(a, b), 0.0);
}

bool isOrthogonal(Point a1, Point a2, Point b1, Point b2)
{
  return isOrthogonal(a1 - a2, b1 - b2);
}

bool isOrthogonal(Segment s1, Segment s2)
{
  return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

bool isParallel(Vector a, Vector b)
{
  return equals(cross(a, b), 0.0);
}

bool isParallel(Point a1, Point a2, Point b1, Point b2)
{
  return isParallel(a1 - a2, b1 - b2);
}

bool isParallel(Segment s1, Segment s2)
{
  return equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}

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

Point reflect(Segment s, Point p)
{
  return p + (project(s, p) - p) * 2.0;
}

double arg(Vector p)
{
  return atan2(p.y, p.x);
}

Vector polar(double a, double r)
{
  return Point(cos(r) * a, sin(r) * a);
}

int ccw(Point p0, Point p1, Point p2);
bool intersectSS(Point p1, Point p2, Point p3, Point p4);
bool intersectSS(Segment s1, Segment s2);
bool intersectPS(Polygon p, Segment l);
int intersectCC(Circle c1, Circle c2);
bool intersectSC(Segment s, Circle c);
double getDistanceLP(Line l, Point p);
double getDistanceSP(Segment s, Point p);
double getDistanceSS(Segment s1, Segment s2);
Point getCrossPointSS(Segment s1, Segment s2);
Point getCrossPointLL(Line l1, Line l2);
Polygon getCrossPointCL(Circle c, Line l);
Polygon getCrossPointCC(Circle c1, Circle c2);
int contains(Polygon g, Point p);
Polygon andrewScan(Polygon s);
Polygon convex_hull(Polygon ps);
double diameter(Polygon s);
bool isConvex(Polygon p);
double area(Polygon s);
Polygon convexCut(Polygon p, Line l);
Line bisector(Point p1, Point p2);
Vector translate(Vector v, double theta);
vector<Line> corner(Line l1, Line l2);
vector<vector<int>>
segmentArrangement(vector<Segment> &ss, Polygon &ps);

int ccw(Point p0, Point p1, Point p2)
{
  Vector a = p1 - p0;
  Vector b = p2 - p0;
  if (cross(a, b) > EPS)
    return CCW_COUNTER_CLOCKWISE;
  if (cross(a, b) < -EPS)
    return CCW_CLOCKWISE;
  if (dot(a, b) < -EPS)
    return CCW_ONLINE_BACK;
  if (a.norm() < b.norm())
    return CCW_ONLINE_FRONT;
  return CCW_ON_SEGMENT;
}

bool intersectSS(Point p1, Point p2, Point p3, Point p4)
{
  return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
          ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}

bool intersectSS(Segment s1, Segment s2)
{
  return intersectSS(s1.p1, s1.p2, s2.p1, s2.p2);
}

bool intersectPS(Polygon p, Segment l)
{
  int n = p.size();
  for (int i = 0; i < n; i++)
    if (intersectSS(Segment(p[i], p[(i + 1) % n]), l))
      return 1;
  return 0;
}

int intersectCC(Circle c1, Circle c2)
{
  if (c1.r < c2.r)
    swap(c1, c2);
  double d = abs(c1.c - c2.c);
  double r = c1.r + c2.r;
  if (equals(d, r))
    return ICC_CIRCUMSCRIBE;
  if (d > r)
    return ICC_SEPERATE;
  if (equals(d + c2.r, c1.r))
    return ICC_INSCRIBE;
  if (d + c2.r < c1.r)
    return ICC_CONTAIN;
  return ICC_INTERSECT;
}

bool intersectSC(Segment s, Circle c)
{
  return getDistanceSP(s, c.c) <= c.r;
}

int intersectCS(Circle c, Segment s)
{
  if (norm(project(s, c.c) - c.c) - c.r * c.r > EPS)
    return 0;
  double d1 = abs(c.c - s.p1), d2 = abs(c.c - s.p2);
  if (d1 < c.r + EPS && d2 < c.r + EPS)
    return 0;
  if ((d1 < c.r - EPS && d2 > c.r + EPS) || (d1 > c.r + EPS && d2 < c.r - EPS))
    return 1;
  Point h = project(s, c.c);
  if (dot(s.p1 - h, s.p2 - h) < 0)
    return 2;
  return 0;
}

double getDistanceLP(Line l, Point p)
{
  return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
}

double getDistanceSP(Segment s, 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);
}

double getDistanceSS(Segment s1, Segment s2)
{
  if (intersectSS(s1, s2))
    return 0.0;
  return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
             min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

Point getCrossPointSS(Segment s1, Segment s2)
{
  for (int k = 0; k < 2; k++)
  {
    if (getDistanceSP(s1, s2.p1) < EPS)
      return s2.p1;
    if (getDistanceSP(s1, s2.p2) < EPS)
      return s2.p2;
    swap(s1, s2);
  }
  Vector base = s2.p2 - s2.p1;
  double d1 = abs(cross(base, s1.p1 - s2.p1));
  double d2 = abs(cross(base, s1.p2 - s2.p1));
  double t = d1 / (d1 + d2);
  return s1.p1 + (s1.p2 - s1.p1) * t;
}

Point getCrossPointLL(Line l1, Line l2)
{
  double a = cross(l1.p2 - l1.p1, l2.p2 - l2.p1);
  double b = cross(l1.p2 - l1.p1, l1.p2 - l2.p1);
  if (abs(a) < EPS && abs(b) < EPS)
    return l2.p1;
  return l2.p1 + (l2.p2 - l2.p1) * (b / a);
}

Polygon getCrossPointCL(Circle c, Line l)
{
  Polygon ps;
  Point pr = project(l, c.c);
  Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
  if (equals(getDistanceLP(l, c.c), c.r))
  {
    ps.emplace_back(pr);
    return ps;
  }
  double base = sqrt(c.r * c.r - norm(pr - c.c));
  ps.emplace_back(pr + e * base);
  ps.emplace_back(pr - e * base);
  return ps;
}

Polygon getCrossPointCS(Circle c, Segment s)
{
  Line l(s);
  Polygon res = getCrossPointCL(c, l);
  if (intersectCS(c, s) == 2)
    return res;
  if (res.size() > 1u)
  {
    if (dot(l.p1 - res[0], l.p2 - res[0]) > 0)
      swap(res[0], res[1]);
    res.pop_back();
  }
  return res;
}

Polygon getCrossPointCC(Circle c1, Circle c2)
{
  Polygon p(2);
  double d = abs(c1.c - c2.c);
  double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
  double t = arg(c2.c - c1.c);
  p[0] = c1.c + polar(c1.r, t + a);
  p[1] = c1.c + polar(c1.r, t - a);
  return p;
}

// IN:2 ON:1 OUT:0
int contains(Polygon g, Point p)
{
  int n = g.size();
  bool x = false;
  for (int i = 0; i < n; i++)
  {
    Point a = g[i] - p, b = g[(i + 1) % n] - p;
    if (fabs(cross(a, b)) < EPS && dot(a, b) < EPS)
      return 1;
    if (a.y > b.y)
      swap(a, b);
    if (a.y < EPS && EPS < b.y && cross(a, b) > EPS)
      x = !x;
  }
  return (x ? 2 : 0);
}

Polygon andrewScan(Polygon s)
{
  Polygon u, l;
  if (s.size() < 3)
    return s;
  sort(s.begin(), s.end());
  u.push_back(s[0]);
  u.push_back(s[1]);
  l.push_back(s[s.size() - 1]);
  l.push_back(s[s.size() - 2]);
  for (int i = 2; i < (int)s.size(); i++)
  {
    for (int n = u.size();
         n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) != CCW_CLOCKWISE;
         n--)
    {
      u.pop_back();
    }
    u.push_back(s[i]);
  }
  for (int i = s.size() - 3; i >= 0; i--)
  {
    for (int n = l.size();
         n >= 2 && ccw(l[n - 2], l[n - 1], s[i]) != CCW_CLOCKWISE;
         n--)
    {
      l.pop_back();
    }
    l.push_back(s[i]);
  }
  reverse(l.begin(), l.end());
  for (int i = u.size() - 2; i >= 1; i--)
    l.push_back(u[i]);
  return l;
}

Polygon convex_hull(Polygon ps)
{
  int n = ps.size();
  sort(ps.begin(), ps.end(), sort_y);
  int k = 0;
  Polygon qs(n * 2);
  for (int i = 0; i < n; i++)
  {
    while (k > 1 && cross(qs[k - 1] - qs[k - 2], ps[i] - qs[k - 1]) < 0)
      k--;
    qs[k++] = ps[i];
  }
  for (int i = n - 2, t = k; i >= 0; i--)
  {
    while (k > t && cross(qs[k - 1] - qs[k - 2], ps[i] - qs[k - 1]) < 0)
      k--;
    qs[k++] = ps[i];
  }
  qs.resize(k - 1);
  return qs;
}

double diameter(Polygon s)
{
  Polygon p = s;
  int n = p.size();
  if (n == 2)
    return abs(p[0] - p[1]);
  int i = 0, j = 0;
  for (int k = 0; k < n; k++)
  {
    if (p[i] < p[k])
      i = k;
    if (!(p[j] < p[k]))
      j = k;
  }
  double res = 0;
  int si = i, sj = j;
  while (i != sj || j != si)
  {
    res = max(res, abs(p[i] - p[j]));
    if (cross(p[(i + 1) % n] - p[i], p[(j + 1) % n] - p[j]) < 0.0)
    {
      i = (i + 1) % n;
    }
    else
    {
      j = (j + 1) % n;
    }
  }
  return res;
}

bool isConvex(Polygon p)
{
  bool f = 1;
  int n = p.size();
  for (int i = 0; i < n; i++)
  {
    int t = ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]);
    f &= t != CCW_CLOCKWISE;
  }
  return f;
}

double area(Polygon s)
{
  double res = 0;
  for (int i = 0; i < (int)s.size(); i++)
  {
    res += cross(s[i], s[(i + 1) % s.size()]) / 2.0;
  }
  return res;
}

double area(Circle c1, Circle c2)
{
  double d = abs(c1.c - c2.c);
  if (c1.r + c2.r <= d + EPS)
    return 0;
  if (d <= abs(c1.r - c2.r))
  {
    double r = min(c1.r, c2.r);
    return PI * r * r;
  }
  double res = 0;
  for (int k = 0; k < 2; k++)
  {
    double rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d * c1.r);
    double th = acosl(rc) * 2;
    res += (th - sinl(th)) * c1.r * c1.r / 2;
    swap(c1, c2);
  }
  return res;
}

Polygon convexCut(Polygon p, Line l)
{
  Polygon q;
  for (int i = 0; i < (int)p.size(); i++)
  {
    Point a = p[i], b = p[(i + 1) % p.size()];
    if (ccw(l.p1, l.p2, a) != -1)
      q.push_back(a);
    if (ccw(l.p1, l.p2, a) * ccw(l.p1, l.p2, b) < 0)
      q.push_back(getCrossPointLL(Line(a, b), l));
  }
  return q;
}

Line bisector(Point p1, Point p2)
{
  Circle c1 = Circle(p1, abs(p1 - p2)), c2 = Circle(p2, abs(p1 - p2));
  Polygon p = getCrossPointCC(c1, c2);
  if (cross(p2 - p1, p[0] - p1) > 0)
    swap(p[0], p[1]);
  return Line(p[0], p[1]);
}

Vector translate(Vector v, double theta)
{
  Vector res;
  res.x = cos(theta) * v.x - sin(theta) * v.y;
  res.y = sin(theta) * v.x + cos(theta) * v.y;
  return res;
}

vector<Line> corner(Line l1, Line l2)
{
  vector<Line> res;
  if (isParallel(l1, l2))
  {
    double d = getDistanceLP(l1, l2.p1) / 2.0;
    Vector v1 = l1.p2 - l1.p1;
    v1 = v1 / v1.abs() * d;
    Point p = l2.p1 + translate(v1, 90.0 * (PI / 180.0));
    double d1 = getDistanceLP(l1, p);
    double d2 = getDistanceLP(l2, p);
    if (abs(d1 - d2) > d)
    {
      p = l2.p1 + translate(v1, -90.0 * (PI / 180.0));
    }
    res.push_back(Line(p, p + v1));
  }
  else
  {
    Point p = getCrossPointLL(l1, l2);
    Vector v1 = l1.p2 - l1.p1, v2 = l2.p2 - l2.p1;
    v1 = v1 / v1.abs();
    v2 = v2 / v2.abs();
    res.push_back(Line(p, p + (v1 + v2)));
    res.push_back(Line(p, p + translate(v1 + v2, 90.0 * (PI / 180.0))));
  }
  return res;
}

Polygon tangent(Circle c1, Point p2)
{
  Circle c2 = Circle(p2, sqrt(norm(c1.c - p2) - c1.r * c1.r));
  Polygon p = getCrossPointCC(c1, c2);
  sort(p.begin(), p.end());
  return p;
}

vector<Line> tangent(Circle c1, Circle c2)
{
  vector<Line> ls;
  if (c1.r < c2.r)
    swap(c1, c2);
  double g = norm(c1.c - c2.c);
  if (equals(g, 0))
    return ls;
  Point u = (c2.c - c1.c) / sqrt(g);
  Point v = orth(u);
  for (int s = 1; s >= -1; s -= 2)
  {
    double h = (c1.r + s * c2.r) / sqrt(g);
    if (equals(1 - h * h, 0))
    {
      ls.emplace_back(c1.c + u * c1.r, c1.c + (u + v) * c1.r);
    }
    else if (1 - h * h > 0)
    {
      Point uu = u * h, vv = v * sqrt(1 - h * h);
      ls.emplace_back(c1.c + (uu + vv) * c1.r, c2.c - (uu + vv) * c2.r * s);
      ls.emplace_back(c1.c + (uu - vv) * c1.r, c2.c - (uu - vv) * c2.r * s);
    }
  }

  return ls;
}

double closest_pair(Polygon &a, int l = 0, int r = -1)
{
  if (r < 0)
  {
    r = a.size();
    sort(a.begin(), a.end(), sort_x);
  }
  if (r - l <= 1)
    return abs(a[0] - a[1]);
  int m = (l + r) >> 1;
  double x = a[m].x;
  double d = min(closest_pair(a, l, m), closest_pair(a, m, r));
  inplace_merge(a.begin() + l, a.begin() + m, a.begin() + r, sort_y);

  Polygon b;
  for (int i = l; i < r; i++)
  {
    if (fabs(a[i].x - x) >= d)
      continue;
    for (int j = 0; j < (int)b.size(); j++)
    {
      double dy = a[i].y - next(b.rbegin(), j)->y;
      if (dy >= d)
        break;
      d = min(d, abs(a[i] - *next(b.rbegin(), j)));
    }
    b.emplace_back(a[i]);
  }
  return d;
}

vector<vector<int>>
segmentArrangement(vector<Segment> &ss, Polygon &ps)
{
  int n = ss.size();
  for (int i = 0; i < n; i++)
  {
    ps.emplace_back(ss[i].p1);
    ps.emplace_back(ss[i].p2);
    for (int j = i + 1; j < n; j++)
      if (intersectSS(ss[i], ss[j]))
        ps.emplace_back(getCrossPointSS(ss[i], ss[j]));
  }
  sort(ps.begin(), ps.end());
  ps.erase(unique(ps.begin(), ps.end()), ps.end());

  vector<vector<int>> G(ps.size());
  for (int i = 0; i < n; i++)
  {
    vector<pair<double, int>> ls;
    for (int j = 0; j < (int)ps.size(); j++)
      if (getDistanceSP(ss[i], ps[j]) < EPS)
        ls.emplace_back(make_pair(norm(ss[i].p1 - ps[j]), j));

    sort(ls.begin(), ls.end());
    for (int j = 0; j + 1 < (int)ls.size(); j++)
    {
      int a = ls[j].second, b = ls[j + 1].second;
      G[a].emplace_back(b);
      G[b].emplace_back(a);
    }
  }
  for (auto &v : G)
  {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
  }
  return G;
}

int manhattan_intersection(vector<Segment> ss, const int INF)
{
  const int BTM = 0;
  const int LFT = 1;
  const int RGH = 2;
  const int TOP = 3;

  int n = ss.size();
  vector<EndPoint> ep;
  for (int i = 0; i < n; i++)
  {
    if (ss[i].p1.y == ss[i].p2.y)
    {
      if (ss[i].p1.x > ss[i].p2.x)
        swap(ss[i].p1, ss[i].p2);
      ep.emplace_back(ss[i].p1, i, LFT);
      ep.emplace_back(ss[i].p2, i, RGH);
    }
    else
    {
      if (ss[i].p1.y > ss[i].p2.y)
        swap(ss[i].p1, ss[i].p2);
      ep.emplace_back(ss[i].p1, i, BTM);
      ep.emplace_back(ss[i].p2, i, TOP);
    }
  }
  sort(ep.begin(), ep.end());

  set<int> bt;
  bt.insert(INF);

  int cnt = 0;
  for (int i = 0; i < n * 2; i++)
  {
    if (ep[i].st == TOP)
    {
      bt.erase(ep[i].p.x);
    }
    else if (ep[i].st == BTM)
    {
      bt.emplace(ep[i].p.x);
    }
    else if (ep[i].st == LFT)
    {
      auto b = bt.lower_bound(ss[ep[i].seg].p1.x);
      auto e = bt.upper_bound(ss[ep[i].seg].p2.x);
      cnt += distance(b, e);
    }
  }

  return cnt;
}

double area(Polygon ps, Circle c)
{
  if (ps.size() < 3u)
    return 0;
  function<double(Circle, Point, Point)> dfs =
      [&](Circle c, Point a, Point b) {
        Vector va = c.c - a, vb = c.c - b;
        double f = cross(va, vb), res = 0;
        if (equals(f, 0.0))
          return res;
        if (max(abs(va), abs(vb)) < c.r + EPS)
          return f;
        Vector d(dot(va, vb), cross(va, vb));
        if (getDistanceSP(Segment(a, b), c.c) > c.r - EPS)
          return c.r * c.r * atan2(d.y, d.x);
        auto u = getCrossPointCS(c, Segment(a, b));
        if (u.empty())
          return res;
        if (u.size() > 1u && dot(u[1] - u[0], a - u[0]) > 0)
          swap(u[0], u[1]);
        u.emplace(u.begin(), a);
        u.emplace_back(b);
        for (int i = 1; i < (int)u.size(); i++)
          res += dfs(c, u[i - 1], u[i]);
        return res;
      };
  double res = 0;
  for (int i = 0; i < (int)ps.size(); i++)
    res += dfs(c, ps[i], ps[(i + 1) % ps.size()]);
  return res / 2;
}

bool check(vector<double> &x, vector<double> &y, vector<double> &r, int k)
{
  int n = x.size();
  using P = Point;
  vector<P> cond;
  rep(i, n) cond.push_back(P(x[i], y[i]));
  rep(i, n) rep(j, i)
  {
    P p1 = P(x[i], y[i]);
    P p2 = P(x[j], y[j]);
    Circle c1({x[i], y[i]}, r[i]);
    Circle c2({x[j], y[j]}, r[j]);
    if (abs(r[i] - r[j]) > abs(p1 - p2))
      continue;
    if (abs(p1 - p2) > r[i] + r[j])
      continue;
    auto c = getCrossPointCC(c1, c2);
    cond.push_back(c[0]);
    cond.push_back(c[1]);
  }
  for (auto s : cond)
  {
    int ans = 0;
    rep(i, n)
    {
      P p(x[i], y[i]);
      if (abs(s - p) <= r[i] + 1e-9)
      {
        ans++;
      }
    }
    if (ans >= k)
      return true;
  }
  return false;
}

void solve(long long N, long long K, std::vector<long long> x,
           std::vector<long long> y, std::vector<long long> c)
{
  vector<double> X(N), Y(N), C(N);
  rep(i, N) Y[i] = y[i], X[i] = x[i], C[i] = c[i];
  double up = 1e10, low = 0;
  rep(I, 200)
  {
    double mid = (up + low) / 2.0;
    auto CC = C;
    rep(i, N) CC[i] = mid / CC[i];
    // cerr << up << " " << low << endl;
    if (check(X, Y, CC, K))
      up = mid;
    else
      low = mid;
  }
  printf("%.10f\n", up);
}

int main()
{
  long long N;
  scanf("%lld", &N);
  long long K;
  scanf("%lld", &K);
  std::vector<long long> x(N);
  std::vector<long long> y(N);
  std::vector<long long> c(N);
  for (int i = 0; i < N; i++)
  {
    scanf("%lld", &x[i]);
    scanf("%lld", &y[i]);
    scanf("%lld", &c[i]);
  }
  solve(N, K, std::move(x), std::move(y), std::move(c));
  return 0;
}

// -- lib
void YESNO(bool b) { cout << (b ? "YES" : "NO") << endl; }
void YesNo(bool b) { cout << (b ? "Yes" : "No") << endl; }

template <class T1, class T2>
bool chmin(T1 &l, const T2 &r)
{
  return (l > r) ? (l = r, true) : false;
}

template <class T1, class T2>
bool chmax(T1 &l, const T2 &r)
{
  return (l < r) ? (l = r, true) : false;
}

Measured memory_bytes: 384