Problem: In the year of 3000 travelling around parallel realities became a routine thing. However one has to take into consideration that travelling like that is highly dangerous as you never know beforehand where you're gonna get...

Little Vasya, for instance, found himself in a gaming reality and now he has to successfully complete all levels of a very weird game to get back. The gaming reality is a three-dimensional space where n points are given. The game has m levels and at the beginning of the i-th level the player is positioned at some plane Qi that passes through the origin. On each level Vasya has to use special robots to construct and activate n powerful energy spheres of the equal radius with centers at the given points. The player chooses the radius of the spheres himself. The player has to spend R units of money to construct spheres whose radius equals R (consequently, one can construct spheres whose radius equals zero for free). Besides, once for each level a player can choose any point in space and release a laser ray from there, perpendicular to plane Qi (this action costs nothing). The ray can either be directed towards the plane or from the plane. The spheres that share at least one point with the ray will be immediately activated. The level is considered completed if the player has managed to activate all spheres. Note that the centers of the spheres are the same for all m levels but the spheres do not remain: the player should construct them anew on each new level.

Help Vasya find out what minimum sum of money will be enough to complete each level.

Input

The first line contains two integers n and m (1 ≤ n ≤ 900, 1 ≤ m ≤ 100) — the number of energetic spheres and the number of levels in the game correspondingly. 

Each of the following n lines contains three integers xi, yi, zi (0 ≤ xi, yi, zi ≤ 104) — the coordinates of the center of the i-th sphere. Assume that these points do not change their positions throughout the game.

Then follow m lines, each containing three integers ai, bi, ci (0 ≤ ai, bi, ci ≤ 100, ai2 + bi2 + ci2 > 0). These numbers are the coefficients in the equation of plane Qi (aix + biy + ciz = 0), where the player is positioned at the beginning of the i-th level.

Output

Print m numbers, one per line: the i-th line should contain the minimum sum of money needed to complete the i-th level. The absolute or relative error should not exceed 10 - 6.

Examples

Input

4 1
0 0 0
0 1 0
1 0 0
1 1 0
0 0 1


Output

0.7071067812


Input

5 3
0 1 0
1 0 1
1 2 1
2 0 1
1 3 0
1 1 1
1 2 3
3 0 3


Output

1.6329931619
1.6366341768
1.5411035007


Input

2 1
0 20 0
0 0 0
0 10 0


Output

0.0000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
const double inf = 1e20;
const double pi = acos(-1.0);
const int maxp = 1111;
int dblcmp(double d) {
  if (fabs(d) < eps) return 0;
  return d > eps ? 1 : -1;
}
inline double sqr(double x) { return x * x; }
struct point {
  double x, y;
  point() {}
  point(double _x, double _y) : x(_x), y(_y){};
  void input() { scanf("%lf%lf", &x, &y); }
  void output() { printf("%.2f %.2f\n", x, y); }
  bool operator==(point a) const {
    return dblcmp(a.x - x) == 0 && dblcmp(a.y - y) == 0;
  }
  bool operator<(point a) const {
    return dblcmp(a.x - x) == 0 ? dblcmp(y - a.y) < 0 : x < a.x;
  }
  double len() { return hypot(x, y); }
  double len2() { return x * x + y * y; }
  double distance(point p) { return hypot(x - p.x, y - p.y); }
  point add(point p) { return point(x + p.x, y + p.y); }
  point sub(point p) { return point(x - p.x, y - p.y); }
  point mul(double b) { return point(x * b, y * b); }
  point div(double b) { return point(x / b, y / b); }
  double dot(point p) { return x * p.x + y * p.y; }
  double det(point p) { return x * p.y - y * p.x; }
  double rad(point a, point b) {
    point p = *this;
    return fabs(atan2(fabs(a.sub(p).det(b.sub(p))), a.sub(p).dot(b.sub(p))));
  }
  point trunc(double r) {
    double l = len();
    if (!dblcmp(l)) return *this;
    r /= l;
    return point(x * r, y * r);
  }
  point rotleft() { return point(-y, x); }
  point rotright() { return point(y, -x); }
  point rotate(point p, double angle) {
    point v = this->sub(p);
    double c = cos(angle), s = sin(angle);
    return point(p.x + v.x * c - v.y * s, p.y + v.x * s + v.y * c);
  }
};
struct line {
  point a, b;
  line() {}
  line(point _a, point _b) {
    a = _a;
    b = _b;
  }
  bool operator==(line v) { return (a == v.a) && (b == v.b); }
  line(point p, double angle) {
    a = p;
    if (dblcmp(angle - pi / 2) == 0) {
      b = a.add(point(0, 1));
    } else {
      b = a.add(point(1, tan(angle)));
    }
  }
  line(double _a, double _b, double _c) {
    if (dblcmp(_a) == 0) {
      a = point(0, -_c / _b);
      b = point(1, -_c / _b);
    } else if (dblcmp(_b) == 0) {
      a = point(-_c / _a, 0);
      b = point(-_c / _a, 1);
    } else {
      a = point(0, -_c / _b);
      b = point(1, (-_c - _a) / _b);
    }
  }
  void input() {
    a.input();
    b.input();
  }
  void adjust() {
    if (b < a) swap(a, b);
  }
  double length() { return a.distance(b); }
  double angle() {
    double k = atan2(b.y - a.y, b.x - a.x);
    if (dblcmp(k) < 0) k += pi;
    if (dblcmp(k - pi) == 0) k -= pi;
    return k;
  }
  int relation(point p) {
    int c = dblcmp(p.sub(a).det(b.sub(a)));
    if (c < 0) return 1;
    if (c > 0) return 2;
    return 3;
  }
  bool pointonseg(point p) {
    return dblcmp(p.sub(a).det(b.sub(a))) == 0 &&
           dblcmp(p.sub(a).dot(p.sub(b))) <= 0;
  }
  bool parallel(line v) { return dblcmp(b.sub(a).det(v.b.sub(v.a))) == 0; }
  int segcrossseg(line v) {
    int d1 = dblcmp(b.sub(a).det(v.a.sub(a)));
    int d2 = dblcmp(b.sub(a).det(v.b.sub(a)));
    int d3 = dblcmp(v.b.sub(v.a).det(a.sub(v.a)));
    int d4 = dblcmp(v.b.sub(v.a).det(b.sub(v.a)));
    if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 2;
    return (d1 == 0 && dblcmp(v.a.sub(a).dot(v.a.sub(b))) <= 0 ||
            d2 == 0 && dblcmp(v.b.sub(a).dot(v.b.sub(b))) <= 0 ||
            d3 == 0 && dblcmp(a.sub(v.a).dot(a.sub(v.b))) <= 0 ||
            d4 == 0 && dblcmp(b.sub(v.a).dot(b.sub(v.b))) <= 0);
  }
  int linecrossseg(line v) {
    int d1 = dblcmp(b.sub(a).det(v.a.sub(a)));
    int d2 = dblcmp(b.sub(a).det(v.b.sub(a)));
    if ((d1 ^ d2) == -2) return 2;
    return (d1 == 0 || d2 == 0);
  }
  int linecrossline(line v) {
    if ((*this).parallel(v)) {
      return v.relation(a) == 3;
    }
    return 2;
  }
  point crosspoint(line v) {
    double a1 = v.b.sub(v.a).det(a.sub(v.a));
    double a2 = v.b.sub(v.a).det(b.sub(v.a));
    return point((a.x * a2 - b.x * a1) / (a2 - a1),
                 (a.y * a2 - b.y * a1) / (a2 - a1));
  }
  double dispointtoline(point p) {
    return fabs(p.sub(a).det(b.sub(a))) / length();
  }
  double dispointtoseg(point p) {
    if (dblcmp(p.sub(b).dot(a.sub(b))) < 0 ||
        dblcmp(p.sub(a).dot(b.sub(a))) < 0) {
      return min(p.distance(a), p.distance(b));
    }
    return dispointtoline(p);
  }
  point lineprog(point p) {
    return a.add(b.sub(a).mul(b.sub(a).dot(p.sub(a)) / b.sub(a).len2()));
  }
  point symmetrypoint(point p) {
    point q = lineprog(p);
    return point(2 * q.x - p.x, 2 * q.y - p.y);
  }
};
struct circle {
  point p;
  double r;
  circle() {}
  circle(point _p, double _r) : p(_p), r(_r){};
  circle(double x, double y, double _r) : p(point(x, y)), r(_r){};
  circle(point a, point b, point c) {
    p = line(a.add(b).div(2), a.add(b).div(2).add(b.sub(a).rotleft()))
            .crosspoint(
                line(c.add(b).div(2), c.add(b).div(2).add(b.sub(c).rotleft())));
    r = p.distance(a);
  }
  circle(point a, point b, point c, bool t) {
    line u, v;
    double m = atan2(b.y - a.y, b.x - a.x), n = atan2(c.y - a.y, c.x - a.x);
    u.a = a;
    u.b = u.a.add(point(cos((n + m) / 2), sin((n + m) / 2)));
    v.a = b;
    m = atan2(a.y - b.y, a.x - b.x), n = atan2(c.y - b.y, c.x - b.x);
    v.b = v.a.add(point(cos((n + m) / 2), sin((n + m) / 2)));
    p = u.crosspoint(v);
    r = line(a, b).dispointtoseg(p);
  }
  void input() {
    p.input();
    scanf("%lf", &r);
  }
  void output() { printf("%.2lf %.2lf %.2lf\n", p.x, p.y, r); }
  bool operator==(circle v) { return ((p == v.p) && dblcmp(r - v.r) == 0); }
  bool operator<(circle v) const {
    return ((p < v.p) || (p == v.p) && dblcmp(r - v.r) < 0);
  }
  double area() { return pi * sqr(r); }
  double circumference() { return 2 * pi * r; }
  int relation(point b) {
    double dst = b.distance(p);
    if (dblcmp(dst - r) < 0) return 2;
    if (dblcmp(dst - r) == 0) return 1;
    return 0;
  }
  int relationseg(line v) {
    double dst = v.dispointtoseg(p);
    if (dblcmp(dst - r) < 0) return 2;
    if (dblcmp(dst - r) == 0) return 1;
    return 0;
  }
  int relationline(line v) {
    double dst = v.dispointtoline(p);
    if (dblcmp(dst - r) < 0) return 2;
    if (dblcmp(dst - r) == 0) return 1;
    return 0;
  }
  int getcircle(point a, point b, double r, circle &c1, circle &c2) {
    circle x(a, r), y(b, r);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r;
    return t;
  }
  int getcircle(line u, point q, double r1, circle &c1, circle &c2) {
    double dis = u.dispointtoline(q);
    if (dblcmp(dis - r1 * 2) > 0) return 0;
    if (dblcmp(dis) == 0) {
      c1.p = q.add(u.b.sub(u.a).rotleft().trunc(r1));
      c2.p = q.add(u.b.sub(u.a).rotright().trunc(r1));
      c1.r = c2.r = r1;
      return 2;
    }
    line u1 = line(u.a.add(u.b.sub(u.a).rotleft().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotleft().trunc(r1)));
    line u2 = line(u.a.add(u.b.sub(u.a).rotright().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotright().trunc(r1)));
    circle cc = circle(q, r1);
    point p1, p2;
    if (!cc.pointcrossline(u1, p1, p2)) cc.pointcrossline(u2, p1, p2);
    c1 = circle(p1, r1);
    if (p1 == p2) {
      c2 = c1;
      return 1;
    }
    c2 = circle(p2, r1);
    return 2;
  }
  int getcircle(line u, line v, double r1, circle &c1, circle &c2, circle &c3,
                circle &c4) {
    if (u.parallel(v)) return 0;
    line u1 = line(u.a.add(u.b.sub(u.a).rotleft().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotleft().trunc(r1)));
    line u2 = line(u.a.add(u.b.sub(u.a).rotright().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotright().trunc(r1)));
    line v1 = line(v.a.add(v.b.sub(v.a).rotleft().trunc(r1)),
                   v.b.add(v.b.sub(v.a).rotleft().trunc(r1)));
    line v2 = line(v.a.add(v.b.sub(v.a).rotright().trunc(r1)),
                   v.b.add(v.b.sub(v.a).rotright().trunc(r1)));
    c1.r = c2.r = c3.r = c4.r = r1;
    c1.p = u1.crosspoint(v1);
    c2.p = u1.crosspoint(v2);
    c3.p = u2.crosspoint(v1);
    c4.p = u2.crosspoint(v2);
    return 4;
  }
  int getcircle(circle cx, circle cy, double r1, circle &c1, circle &c2) {
    circle x(cx.p, r1 + cx.r), y(cy.p, r1 + cy.r);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r1;
    return t;
  }
  int pointcrossline(line v, point &p1, point &p2) {
    if (!(*this).relationline(v)) return 0;
    point a = v.lineprog(p);
    double d = v.dispointtoline(p);
    d = sqrt(r * r - d * d);
    if (dblcmp(d) == 0) {
      p1 = a;
      p2 = a;
      return 1;
    }
    p1 = a.sub(v.b.sub(v.a).trunc(d));
    p2 = a.add(v.b.sub(v.a).trunc(d));
    return 2;
  }
  int relationcircle(circle v) {
    double d = p.distance(v.p);
    if (dblcmp(d - r - v.r) > 0) return 5;
    if (dblcmp(d - r - v.r) == 0) return 4;
    double l = fabs(r - v.r);
    if (dblcmp(d - r - v.r) < 0 && dblcmp(d - l) > 0) return 3;
    if (dblcmp(d - l) == 0) return 2;
    if (dblcmp(d - l) < 0) return 1;
  }
  int pointcrosscircle(circle v, point &p1, point &p2) {
    int rel = relationcircle(v);
    if (rel == 1 || rel == 5) return 0;
    double d = p.distance(v.p);
    double l = (d + (sqr(r) - sqr(v.r)) / d) / 2;
    double h = sqrt(sqr(r) - sqr(l));
    p1 = p.add(v.p.sub(p).trunc(l).add(v.p.sub(p).rotleft().trunc(h)));
    p2 = p.add(v.p.sub(p).trunc(l).add(v.p.sub(p).rotright().trunc(h)));
    if (rel == 2 || rel == 4) {
      return 1;
    }
    return 2;
  }
  int tangentline(point q, line &u, line &v) {
    int x = relation(q);
    if (x == 2) return 0;
    if (x == 1) {
      u = line(q, q.add(q.sub(p).rotleft()));
      v = u;
      return 1;
    }
    double d = p.distance(q);
    double l = sqr(r) / d;
    double h = sqrt(sqr(r) - sqr(l));
    u = line(q, p.add(q.sub(p).trunc(l).add(q.sub(p).rotleft().trunc(h))));
    v = line(q, p.add(q.sub(p).trunc(l).add(q.sub(p).rotright().trunc(h))));
    return 2;
  }
  double areacircle(circle v) {
    int rel = relationcircle(v);
    if (rel >= 4) return 0.0;
    if (rel <= 2) return min(area(), v.area());
    double d = p.distance(v.p);
    double hf = (r + v.r + d) / 2.0;
    double ss = 2 * sqrt(hf * (hf - r) * (hf - v.r) * (hf - d));
    double a1 = acos((r * r + d * d - v.r * v.r) / (2.0 * r * d));
    a1 = a1 * r * r;
    double a2 = acos((v.r * v.r + d * d - r * r) / (2.0 * v.r * d));
    a2 = a2 * v.r * v.r;
    return a1 + a2 - ss;
  }
  double areatriangle(point a, point b) {
    if (dblcmp(p.sub(a).det(p.sub(b)) == 0)) return 0.0;
    point q[5];
    int len = 0;
    q[len++] = a;
    line l(a, b);
    point p1, p2;
    if (pointcrossline(l, q[1], q[2]) == 2) {
      if (dblcmp(a.sub(q[1]).dot(b.sub(q[1]))) < 0) q[len++] = q[1];
      if (dblcmp(a.sub(q[2]).dot(b.sub(q[2]))) < 0) q[len++] = q[2];
    }
    q[len++] = b;
    if (len == 4 && (dblcmp(q[0].sub(q[1]).dot(q[2].sub(q[1]))) > 0))
      swap(q[1], q[2]);
    double res = 0;
    int i;
    for (i = 0; i < len - 1; i++) {
      if (relation(q[i]) == 0 || relation(q[i + 1]) == 0) {
        double arg = p.rad(q[i], q[i + 1]);
        res += r * r * arg / 2.0;
      } else {
        res += fabs(q[i].sub(p).det(q[i + 1].sub(p)) / 2.0);
      }
    }
    return res;
  }
};
struct polygon {
  int n;
  point p[maxp];
  line l[maxp];
  void input() {
    for (int i = 0; i < n; i++) {
      p[i].input();
    }
  }
  void add(point q) { p[n++] = q; }
  void getline() {
    for (int i = 0; i < n; i++) {
      l[i] = line(p[i], p[(i + 1) % n]);
    }
  }
  struct cmp {
    point p;
    cmp(const point &p0) { p = p0; }
    bool operator()(const point &aa, const point &bb) {
      point a = aa, b = bb;
      int d = dblcmp(a.sub(p).det(b.sub(p)));
      if (d == 0) {
        return dblcmp(a.distance(p) - b.distance(p)) < 0;
      }
      return d > 0;
    }
  };
  void norm() {
    point mi = p[0];
    for (int i = 1; i < n; i++) mi = min(mi, p[i]);
    sort(p, p + n, cmp(mi));
  }
  void getconvex(polygon &convex) {
    int i, j, k;
    sort(p, p + n);
    convex.n = n;
    for (i = 0; i < min(n, 2); i++) {
      convex.p[i] = p[i];
    }
    if (n <= 2) return;
    int &top = convex.n;
    top = 1;
    for (i = 2; i < n; i++) {
      while (top &&
             convex.p[top].sub(p[i]).det(convex.p[top - 1].sub(p[i])) <= 0)
        top--;
      convex.p[++top] = p[i];
    }
    int temp = top;
    convex.p[++top] = p[n - 2];
    for (i = n - 3; i >= 0; i--) {
      while (top != temp &&
             convex.p[top].sub(p[i]).det(convex.p[top - 1].sub(p[i])) <= 0)
        top--;
      convex.p[++top] = p[i];
    }
  }
  bool isconvex() {
    bool s[3];
    memset(s, 0, sizeof(s));
    int i, j, k;
    for (i = 0; i < n; i++) {
      j = (i + 1) % n;
      k = (j + 1) % n;
      s[dblcmp(p[j].sub(p[i]).det(p[k].sub(p[i]))) + 1] = 1;
      if (s[0] && s[2]) return 0;
    }
    return 1;
  }
  int relationpoint(point q) {
    int i, j;
    for (i = 0; i < n; i++) {
      if (p[i] == q) return 3;
    }
    getline();
    for (i = 0; i < n; i++) {
      if (l[i].pointonseg(q)) return 2;
    }
    int cnt = 0;
    for (i = 0; i < n; i++) {
      j = (i + 1) % n;
      int k = dblcmp(q.sub(p[j]).det(p[i].sub(p[j])));
      int u = dblcmp(p[i].y - q.y);
      int v = dblcmp(p[j].y - q.y);
      if (k > 0 && u < 0 && v >= 0) cnt++;
      if (k < 0 && v < 0 && u >= 0) cnt--;
    }
    return cnt != 0;
  }
  int relationline(line u) {
    int i, j, k = 0;
    getline();
    for (i = 0; i < n; i++) {
      if (l[i].segcrossseg(u) == 2) return 1;
      if (l[i].segcrossseg(u) == 1) k = 1;
    }
    if (!k) return 0;
    vector<point> vp;
    for (i = 0; i < n; i++) {
      if (l[i].segcrossseg(u)) {
        if (l[i].parallel(u)) {
          vp.push_back(u.a);
          vp.push_back(u.b);
          vp.push_back(l[i].a);
          vp.push_back(l[i].b);
          continue;
        }
        vp.push_back(l[i].crosspoint(u));
      }
    }
    sort(vp.begin(), vp.end());
    int sz = vp.size();
    for (i = 0; i < sz - 1; i++) {
      point mid = vp[i].add(vp[i + 1]).div(2);
      if (relationpoint(mid) == 1) return 1;
    }
    return 2;
  }
  void convexcut(line u, polygon &po) {
    int i, j, k;
    int &top = po.n;
    top = 0;
    for (i = 0; i < n; i++) {
      int d1 = dblcmp(p[i].sub(u.a).det(u.b.sub(u.a)));
      int d2 = dblcmp(p[(i + 1) % n].sub(u.a).det(u.b.sub(u.a)));
      if (d1 >= 0) po.p[top++] = p[i];
      if (d1 * d2 < 0) po.p[top++] = u.crosspoint(line(p[i], p[(i + 1) % n]));
    }
  }
  double getcircumference() {
    double sum = 0;
    int i;
    for (i = 0; i < n; i++) {
      sum += p[i].distance(p[(i + 1) % n]);
    }
    return sum;
  }
  double getarea() {
    double sum = 0;
    int i;
    for (i = 0; i < n; i++) {
      sum += p[i].det(p[(i + 1) % n]);
    }
    return fabs(sum) / 2;
  }
  bool getdir() {
    double sum = 0;
    int i;
    for (i = 0; i < n; i++) {
      sum += p[i].det(p[(i + 1) % n]);
    }
    if (dblcmp(sum) > 0) return 1;
    return 0;
  }
  point getbarycentre() {
    point ret(0, 0);
    double area = 0;
    int i;
    for (i = 1; i < n - 1; i++) {
      double tmp = p[i].sub(p[0]).det(p[i + 1].sub(p[0]));
      if (dblcmp(tmp) == 0) continue;
      area += tmp;
      ret.x += (p[0].x + p[i].x + p[i + 1].x) / 3 * tmp;
      ret.y += (p[0].y + p[i].y + p[i + 1].y) / 3 * tmp;
    }
    if (dblcmp(area)) ret = ret.div(area);
    return ret;
  }
  double areaintersection(polygon po) {}
  double areaunion(polygon po) {
    return getarea() + po.getarea() - areaintersection(po);
  }
  double areacircle(circle c) {
    int i, j, k, l, m;
    double ans = 0;
    for (i = 0; i < n; i++) {
      int j = (i + 1) % n;
      if (dblcmp(p[j].sub(c.p).det(p[i].sub(c.p))) >= 0) {
        ans += c.areatriangle(p[i], p[j]);
      } else {
        ans -= c.areatriangle(p[i], p[j]);
      }
    }
    return fabs(ans);
  }
  int relationcircle(circle c) {
    getline();
    int i, x = 2;
    if (relationpoint(c.p) != 1) return 0;
    for (i = 0; i < n; i++) {
      if (c.relationseg(l[i]) == 2) return 0;
      if (c.relationseg(l[i]) == 1) x = 1;
    }
    return x;
  }
  int circlecover(double r) {
    int ans = 0, i, j;
    vector<pair<double, int> > v;
    for (i = 0; i < n; i++) {
      v.clear();
      for (j = 0; j < n; j++)
        if (i != j) {
          point q = p[i].sub(p[j]);
          double d = q.len();
          if (dblcmp(d - 2 * r) <= 0) {
            double arg = atan2(q.y, q.x);
            if (dblcmp(arg) < 0) arg += 2 * pi;
            double t = acos(d / (2 * r));
            v.push_back(make_pair(arg - t + 2 * pi, -1));
            v.push_back(make_pair(arg + t + 2 * pi, 1));
          }
        }
      sort(v.begin(), v.end());
      int cur = 0;
      for (j = 0; j < v.size(); j++) {
        if (v[j].second == -1)
          ++cur;
        else
          --cur;
        ans = max(ans, cur);
      }
    }
    return ans + 1;
  }
  int pointinpolygon(point q) {
    if (getdir()) reverse(p, p + n);
    if (dblcmp(q.sub(p[0]).det(p[n - 1].sub(p[0]))) == 0) {
      if (line(p[n - 1], p[0]).pointonseg(q)) return n - 1;
      return -1;
    }
    int low = 1, high = n - 2, mid;
    while (low <= high) {
      mid = (low + high) >> 1;
      if (dblcmp(q.sub(p[0]).det(p[mid].sub(p[0]))) >= 0 &&
          dblcmp(q.sub(p[0]).det(p[mid + 1].sub(p[0]))) < 0) {
        polygon c;
        c.p[0] = p[mid];
        c.p[1] = p[mid + 1];
        c.p[2] = p[0];
        c.n = 3;
        if (c.relationpoint(q)) return mid;
        return -1;
      }
      if (dblcmp(q.sub(p[0]).det(p[mid].sub(p[0]))) > 0) {
        low = mid + 1;
      } else {
        high = mid - 1;
      }
    }
    return -1;
  }
};
point p[1111];
int n;
void find(int st, point tri[], circle &c) {
  if (!st) {
    c = circle(point(0, 0), -2);
  }
  if (st == 1) {
    c = circle(tri[0], 0);
  }
  if (st == 2) {
    c = circle(tri[0].add(tri[1]).div(2), tri[0].distance(tri[1]) / 2.0);
  }
  if (st == 3) {
    c = circle(tri[0], tri[1], tri[2]);
  }
}
void solve(int cur, int st, point tri[], circle &c) {
  find(st, tri, c);
  if (st == 3) return;
  int i;
  for (i = 0; i < cur; i++) {
    if (dblcmp(p[i].distance(c.p) - c.r) > 0) {
      tri[st] = p[i];
      solve(i, st + 1, tri, c);
    }
  }
}
circle mincircle() {
  random_shuffle(p, p + n);
  point tri[4];
  circle c;
  solve(n, 0, tri, c);
  return c;
}
const int maxn = 500;
struct circles {
  circle c[maxn];
  double ans[maxn];
  double pre[maxn];
  int n;
  circles() {}
  void add(circle cc) { c[n++] = cc; }
  bool inner(circle x, circle y) {
    if (x.relationcircle(y) != 1) return 0;
    return dblcmp(x.r - y.r) <= 0 ? 1 : 0;
  }
  void init_or() {
    int i, j, k = 0;
    bool mark[maxn] = {0};
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++)
        if (i != j && !mark[j]) {
          if ((c[i] == c[j]) || inner(c[i], c[j])) break;
        }
      if (j < n) mark[i] = 1;
    }
    for (i = 0; i < n; i++)
      if (!mark[i]) c[k++] = c[i];
    n = k;
  }
  void init_and() {
    int i, j, k = 0;
    bool mark[maxn] = {0};
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++)
        if (i != j && !mark[j]) {
          if ((c[i] == c[j]) || inner(c[j], c[i])) break;
        }
      if (j < n) mark[i] = 1;
    }
    for (i = 0; i < n; i++)
      if (!mark[i]) c[k++] = c[i];
    n = k;
  }
  double areaarc(double th, double r) { return 0.5 * sqr(r) * (th - sin(th)); }
  void getarea() {
    int i, j, k;
    memset(ans, 0, sizeof(ans));
    vector<pair<double, int> > v;
    for (i = 0; i < n; i++) {
      v.clear();
      v.push_back(make_pair(-pi, 1));
      v.push_back(make_pair(pi, -1));
      for (j = 0; j < n; j++)
        if (i != j) {
          point q = c[j].p.sub(c[i].p);
          double ab = q.len(), ac = c[i].r, bc = c[j].r;
          if (dblcmp(ab + ac - bc) <= 0) {
            v.push_back(make_pair(-pi, 1));
            v.push_back(make_pair(pi, -1));
            continue;
          }
          if (dblcmp(ab + bc - ac) <= 0) continue;
          if (dblcmp(ab - ac - bc) > 0) continue;
          double th = atan2(q.y, q.x),
                 fai = acos((ac * ac + ab * ab - bc * bc) / (2.0 * ac * ab));
          double a0 = th - fai;
          if (dblcmp(a0 + pi) < 0) a0 += 2 * pi;
          double a1 = th + fai;
          if (dblcmp(a1 - pi) > 0) a1 -= 2 * pi;
          if (dblcmp(a0 - a1) > 0) {
            v.push_back(make_pair(a0, 1));
            v.push_back(make_pair(pi, -1));
            v.push_back(make_pair(-pi, 1));
            v.push_back(make_pair(a1, -1));
          } else {
            v.push_back(make_pair(a0, 1));
            v.push_back(make_pair(a1, -1));
          }
        }
      sort(v.begin(), v.end());
      int cur = 0;
      for (j = 0; j < v.size(); j++) {
        if (cur && dblcmp(v[j].first - pre[cur])) {
          ans[cur] += areaarc(v[j].first - pre[cur], c[i].r);
          ans[cur] +=
              0.5 * point(c[i].p.x + c[i].r * cos(pre[cur]),
                          c[i].p.y + c[i].r * sin(pre[cur]))
                        .det(point(c[i].p.x + c[i].r * cos(v[j].first),
                                   c[i].p.y + c[i].r * sin(v[j].first)));
        }
        cur += v[j].second;
        pre[cur] = v[j].first;
      }
    }
    for (i = 1; i <= n; i++) {
      ans[i] -= ans[i + 1];
    }
  }
};
struct halfplane : public line {
  double angle;
  halfplane() {}
  halfplane(point _a, point _b) {
    a = _a;
    b = _b;
  }
  halfplane(line v) {
    a = v.a;
    b = v.b;
  }
  void calcangle() { angle = atan2(b.y - a.y, b.x - a.x); }
  bool operator<(const halfplane &b) const { return angle < b.angle; }
};
struct halfplanes {
  int n;
  halfplane hp[maxp];
  point p[maxp];
  int que[maxp];
  int st, ed;
  void push(halfplane tmp) { hp[n++] = tmp; }
  void unique() {
    int m = 1, i;
    for (i = 1; i < n; i++) {
      if (dblcmp(hp[i].angle - hp[i - 1].angle))
        hp[m++] = hp[i];
      else if (dblcmp(
                   hp[m - 1].b.sub(hp[m - 1].a).det(hp[i].a.sub(hp[m - 1].a)) >
                   0))
        hp[m - 1] = hp[i];
    }
    n = m;
  }
  bool halfplaneinsert() {
    int i;
    for (i = 0; i < n; i++) hp[i].calcangle();
    sort(hp, hp + n);
    unique();
    que[st = 0] = 0;
    que[ed = 1] = 1;
    p[1] = hp[0].crosspoint(hp[1]);
    for (i = 2; i < n; i++) {
      while (st < ed &&
             dblcmp((hp[i].b.sub(hp[i].a).det(p[ed].sub(hp[i].a)))) < 0)
        ed--;
      while (st < ed &&
             dblcmp((hp[i].b.sub(hp[i].a).det(p[st + 1].sub(hp[i].a)))) < 0)
        st++;
      que[++ed] = i;
      if (hp[i].parallel(hp[que[ed - 1]])) return false;
      p[ed] = hp[i].crosspoint(hp[que[ed - 1]]);
    }
    while (
        st < ed &&
        dblcmp(hp[que[st]].b.sub(hp[que[st]].a).det(p[ed].sub(hp[que[st]].a))) <
            0)
      ed--;
    while (st < ed && dblcmp(hp[que[ed]]
                                 .b.sub(hp[que[ed]].a)
                                 .det(p[st + 1].sub(hp[que[ed]].a))) < 0)
      st++;
    if (st + 1 >= ed) return false;
    return true;
  }
  void getconvex(polygon &con) {
    p[st] = hp[que[st]].crosspoint(hp[que[ed]]);
    con.n = ed - st + 1;
    int j = st, i = 0;
    for (; j <= ed; i++, j++) {
      con.p[i] = p[j];
    }
  }
};
struct point3 {
  double x, y, z;
  point3() {}
  point3(double _x, double _y, double _z) : x(_x), y(_y), z(_z){};
  void input() { scanf("%lf%lf%lf", &x, &y, &z); }
  void output() { printf("%.2lf %.2lf %.2lf\n", x, y, z); }
  bool operator==(point3 a) {
    return dblcmp(a.x - x) == 0 && dblcmp(a.y - y) == 0 && dblcmp(a.z - z) == 0;
  }
  bool operator<(point3 a) const {
    return dblcmp(a.x - x) == 0
               ? dblcmp(y - a.y) == 0 ? dblcmp(z - a.z) < 0 : y < a.y
               : x < a.x;
  }
  double len() { return sqrt(len2()); }
  double len2() { return x * x + y * y + z * z; }
  double distance(point3 p) {
    return sqrt((p.x - x) * (p.x - x) + (p.y - y) * (p.y - y) +
                (p.z - z) * (p.z - z));
  }
  point3 add(point3 p) { return point3(x + p.x, y + p.y, z + p.z); }
  point3 sub(point3 p) { return point3(x - p.x, y - p.y, z - p.z); }
  point3 mul(double d) { return point3(x * d, y * d, z * d); }
  point3 div(double d) { return point3(x / d, y / d, z / d); }
  double dot(point3 p) { return x * p.x + y * p.y + z * p.z; }
  point3 det(point3 p) {
    return point3(y * p.z - p.y * z, p.x * z - x * p.z, x * p.y - p.x * y);
  }
  double rad(point3 a, point3 b) {
    point3 p = (*this);
    return acos(a.sub(p).dot(b.sub(p)) / (a.distance(p) * b.distance(p)));
  }
  point3 trunc(double r) {
    r /= len();
    return point3(x * r, y * r, z * r);
  }
  point3 rotate(point3 o, double r) {}
};
struct line3 {
  point3 a, b;
  line3() {}
  line3(point3 _a, point3 _b) {
    a = _a;
    b = _b;
  }
  bool operator==(line3 v) { return (a == v.a) && (b == v.b); }
  void input() {
    a.input();
    b.input();
  }
  double length() { return a.distance(b); }
  double dispointtoline(point3 p) {
    return b.sub(a).det(p.sub(a)).len() / a.distance(b);
  }
  point3 lineprog(point3 p) {
    return a.add(b.sub(a).trunc(b.sub(a).dot(p.sub(a)) / b.distance(a)));
  }
  point3 rotate(point3 p, double ang) {
    if (dblcmp((p.sub(a).det(p.sub(b)).len())) == 0) return p;
    point3 f1 = b.sub(a).det(p.sub(a));
    point3 f2 = b.sub(a).det(f1);
    double len = fabs(a.sub(p).det(b.sub(p)).len() / a.distance(b));
    f1 = f1.trunc(len);
    f2 = f2.trunc(len);
    point3 h = p.add(f2);
    point3 pp = h.add(f1);
    return h.add((p.sub(h)).mul(cos(ang * 1.0)))
        .add((pp.sub(h)).mul(sin(ang * 1.0)));
  }
};
struct plane {
  point3 a, b, c, o;
  plane() {}
  plane(point3 _a, point3 _b, point3 _c) {
    a = _a;
    b = _b;
    c = _c;
    o = pvec();
  }
  plane(double _a, double _b, double _c, double _d) {
    o = point3(_a, _b, _c);
    if (dblcmp(_a) != 0) {
      a = point3((-_d - _c - _b) / _a, 1, 1);
    } else if (dblcmp(_b) != 0) {
      a = point3(1, (-_d - _c - _a) / _b, 1);
    } else if (dblcmp(_c) != 0) {
      a = point3(1, 1, (-_d - _a - _b) / _c);
    }
  }
  void input() {
    a.input();
    b.input();
    c.input();
    o = pvec();
  }
  point3 pvec() { return b.sub(a).det(c.sub(a)); }
  double angleplane(plane f) {
    return acos(o.dot(f.o) / (o.len() * f.o.len()));
  }
  point3 pttoplane(point3 p) {
    line3 u = line3(p, p.add(o));
    crossline(u, p);
    return p;
  }
  int crossline(line3 u, point3 &p) {
    double x = o.dot(u.b.sub(a));
    double y = o.dot(u.a.sub(a));
    double d = x - y;
    if (dblcmp(fabs(d)) == 0) return 0;
    p = u.a.mul(x).sub(u.b.mul(y)).div(d);
    return 1;
  }
  int crossplane(plane f, line3 &u) {
    point3 oo = o.det(f.o);
    point3 v = o.det(oo);
    double d = fabs(f.o.dot(v));
    if (dblcmp(d) == 0) return 0;
    point3 q = a.add(v.mul(f.o.dot(f.a.sub(a)) / d));
    u = line3(q, q.add(oo));
    return 1;
  }
};
plane pf(0, 0, 1, 0);
point3 pp[1120], q[1120], s;
polygon pl;
int main() {
  int i, j, k;
  double a, b, c, d;
  int m;
  scanf("%d%d", &n, &m);
  for (i = 0; i < n; i++) q[i].input();
  for (j = 0; j < m; j++) {
    scanf("%lf%lf%lf", &a, &b, &c);
    plane ps(a, b, c, 0);
    pl.n = 0;
    line3 o;
    for (i = 0; i < n; i++) {
      pp[i] = ps.pttoplane(q[i]);
    }
    if (!ps.crossplane(pf, o)) {
      for (i = 0; i < n; i++) {
        p[i] = (point(pp[i].x, pp[i].y));
      }
    } else {
      double r = ps.angleplane(pf);
      for (i = 0; i < n; i++) {
        point3 ppp = o.rotate(pp[i], r);
        p[i] = (point(ppp.x, ppp.y));
      }
    }
    printf("%.10lf\n", mincircle().r);
  }
  return 0;
}