Problem p01649 (C++) — buggy submission, verdict: Runtime Error

#include <bits/stdc++.h>

#define REP(i, s, n) for (int i = s; i < n; i++)
#define rep(i, n) REP(i, 0, n)
#define EPS (1e-7)
// #define equals(a,b) (fabs((a)-(b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

bool equals(double a, double b, double eps = EPS) {
  return fabs((a) - (b)) < eps;
}

class Point {
public:
  double x, y;

  Point(double x = 0, double y = 0) : 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 a) { return Point(a * x, a * y); }
  Point operator/(double a) { return Point(x / a, y / a); }
  Point operator*(Point a) {
    return Point(x * a.x - y * a.y, x * a.y + y * a.x);
  }

  bool operator<(const Point &p) const {
    return !equals(x, p.x) ? x < p.x : (!equals(y, p.y) && y < p.y);
  }

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

struct Segment {
  Point p1, p2;
  Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
  bool operator<(const Segment &s) const {
    return (p2 == s.p2) ? p1 < s.p1 : p2 < s.p2;
  }
  bool operator==(const Segment &s) const {
    return (s.p1 == p1 && s.p2 == p2) || (s.p1 == p2 && s.p2 == p1);
  }
};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;

ostream &operator<<(ostream &os, const Point &a) {
  os << "(" << a.x << "," << a.y << ")";
}

ostream &operator<<(ostream &os, const Segment &a) {
  os << "( " << a.p1 << " , " << a.p2 << " )";
}

double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }

double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }

double norm(Point a) { return a.x * a.x + a.y * a.y; }

double abs(Point a) { return sqrt(norm(a)); }

int ccw(Point p0, Point p1, Point p2) {
  Point a = p1 - p0;
  Point b = p2 - p0;
  if (cross(a, b) > EPS)
    return COUNTER_CLOCKWISE;
  if (cross(a, b) < -EPS)
    return CLOCKWISE;
  if (dot(a, b) < -EPS)
    return ONLINE_BACK;
  if (norm(a) < norm(b))
    return ONLINE_FRONT;
  return ON_SEGMENT;
}

bool intersectLL(Line l, Line m) {
  return abs(cross(l.p2 - l.p1, m.p2 - m.p1)) > EPS || // non-parallel
         abs(cross(l.p2 - l.p1, m.p1 - l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2 - l.p1, s.p1 - l.p1) * // s[0] is left of l
             cross(l.p2 - l.p1, s.p2 - l.p1) <
         EPS; // s[1] is right of l
}
bool intersectLP(Line l, Point p) {
  return abs(cross(l.p2 - p, l.p1 - p)) < EPS;
}
bool intersectSS(Line s, Line t) {
  return ccw(s.p1, s.p2, t.p1) * ccw(s.p1, s.p2, t.p2) <= 0 &&
         ccw(t.p1, t.p2, s.p1) * ccw(t.p1, t.p2, s.p2) <= 0;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1 - p) + abs(s.p2 - p) - abs(s.p2 - s.p1) <
         EPS; // triangle inequality
}

Point projection(Line l, Point p) {
  double t = dot(p - l.p1, l.p1 - l.p2) / norm(l.p1 - l.p2);
  return l.p1 + (l.p1 - l.p2) * t;
}
Point reflection(Line l, Point p) { return p + (projection(l, p) - p) * 2; }

Point crosspoint(Line l, Line m) {
  double A = cross(l.p2 - l.p1, m.p2 - m.p1);
  double B = cross(l.p2 - l.p1, l.p2 - m.p1);
  if (abs(A) < EPS && abs(B) < EPS) {
    vector<Point> vec;
    vec.push_back(l.p1), vec.push_back(l.p2), vec.push_back(m.p1),
        vec.push_back(m.p2);
    sort(vec.begin(), vec.end());
    assert(vec[1] == vec[2]); // 同じセグメントかもよ
    return vec[1];
    // return m.p1;
  }
  if (abs(A) < EPS)
    assert(false);
  return m.p1 + (m.p2 - m.p1) * (B / A);
}

typedef pair<double, double> dd;
const double DINF = 1e50;
bool LT(double a, double b, double eps = EPS) {
  return !(fabs(a - b) < eps) && a < b;
}
bool LTE(double a, double b, double eps = EPS) {
  return (fabs(a - b) < eps) || a < b;
}
#define pow2(a) ((a) * (a))

dd calc(double x1, double y1, double vx1, double vy1, double x2, double y2,
        double vx2, double vy2, double r) {
  double VX = (vx1 - vx2), X = (x1 - x2), VY = (vy1 - vy2), Y = (y1 - y2);
  double a = pow2(VX) + pow2(VY), b = 2 * (X * VX + Y * VY),
         c = pow2(X) + pow2(Y) - pow2(r);
  dd ret = dd(DINF, DINF);
  double D = b * b - 4 * a * c;

  const double eps = 1e-20;
  if (LT(D, 0.0, eps))
    return ret;

  if (equals(a, 0.0, eps)) {
    if (equals(b, 0.0, eps))
      return ret;
    if (LT(-c / b, 0.0, eps))
      return ret;
    ret.first = -c / b;
    return ret;
  }

  if (equals(D, 0.0, eps))
    D = 0;
  ret.first = (-b - sqrt(D)) / (2 * a);
  ret.second = (-b + sqrt(D)) / (2 * a);
  if (!equals(ret.first, ret.second) && ret.first > ret.second)
    swap(ret.first, ret.second);
  // cout << ret.first << "," << ret.second << endl;
  return ret;
}

const int MAX_N = 20;
const double TIME = 100000000;
int n;
double w, h, r;
Point ps[MAX_N];
Line table[4];
Vector es[4] = {Vector(10, 0), Vector(0, 10), Vector(-10, 0), Vector(0, -10)};

typedef pair<double, int> di;
bool COMP(const di &a, const di &b) {
  if (!equals(a.first, b.first))
    return LT(a.first, b.first);
  return a.second < b.second;
}

bool success = false;

struct Data {
  int index;
  double time;

  Point rp, cp2;
  bool operator<(const Data &data) const {
    if (!equals(time, data.time))
      return LTE(time, data.time);
    if (index != data.index)
      return index < data.index;
    if (!(rp == data.rp))
      return rp < data.rp;
    return cp2 < data.cp2;
  }
};

vector<Data> getReflection(double remain, double vx, double vy, Point cur,
                           Vector &nv) {
  vector<Data> ret, temp;
  Vector v = Vector(vx, vy);
  rep(i, 4) {
    Vector h = es[i] * Vector(0, 1);
    Line line = Line(cur, cur + h);
    Point cp = crosspoint(table[i], line);
    Vector e = (cp - cur) / abs(cp - cur);
    Point ep = cur + e * r;
    Segment seg = Segment(ep, ep + v * TIME);

    if (intersectLS(table[i], seg)) {
      Point cp2 = crosspoint(table[i], seg);
      double timer = abs(cp2 - ep) / abs(v);
      if (equals(timer, 0.0))
        continue;

      Line wall = Line(cp2, cp2 + h);
      Point rp = reflection(wall, ep);
      temp.push_back((Data){i, timer, rp, cp2});
    }
  }
  if (!temp.empty()) {
    sort(temp.begin(), temp.end());
    double mini = temp[0].time;
    if (LT(remain, mini)) {
      mini = remain;
      ret.push_back((Data){-1, mini});
    }
    rep(i, temp.size()) if (equals(mini, temp[i].time)) {
      ret.push_back(temp[i]);
      // nv = ( temp[i].rp - temp[i].cp2 ) / abs( temp[i].rp - temp[i].cp2 );
      nv = (temp[i].rp - temp[i].cp2);
    }
  }
  return ret;
}

void compute(double remain, double vx, double vy, Point cur) {
  if (equals(remain, 0))
    return;
  Vector vtemp = Vector(vx, vy);
  vtemp = vtemp / abs(vtemp);
  vx = vtemp.x, vy = vtemp.y;
  // cout << setiosflags(ios::fixed) << setprecision(13) << Vector(vx,vy) << " "
  // << cur << endl; cout << "remain = " << remain << " v (" << vx << "," << vy
  // << ") ; cp = " << cur  << endl;
  Vector nv = Vector(123, 456);
  vector<Data> ref = getReflection(remain, vx, vy, cur, nv);
  assert(1 <= ref.size() && ref.size() <= 2);
  double timeLimit = ref[0].time;
  // cout << "ref.size() = " << ref.size() << " " << nv << endl;
  // cout << "timeLimit = " << timeLimit  << " => " <<
  // cur+Vector(vx,vy)*timeLimit<< endl;
  vector<Data> collides;
  REP(i, 1, n) {
    dd temp = calc(cur.x, cur.y, vx, vy, ps[i].x, ps[i].y, 0, 0, 2.0 * r);
    vector<double> vec;
    vec.push_back(temp.first), vec.push_back(temp.second);
    double mini = DINF;
    rep(j, vec.size()) if (LTE(0.0, vec[j]) && LTE(vec[j], timeLimit)) mini =
        min(mini, vec[j]);
    if (!equals(mini, DINF))
      collides.push_back((Data){i, mini});
    // cout << "ball " << i << " : " << temp.first << "," << temp.second <<
    // endl;
  }
  if (!collides.empty()) {
    sort(collides.begin(), collides.end());
    Point temp = cur + Vector(vx, vy) * collides[0].time;
    // cout << collides[0].time << " " << setiosflags(ios::fixed) <<
    // setprecision(10) << (temp-ps[1]) << endl; cout << "remain = " <<
    // collides[0].time << endl;
    printf("%d\\n", collides[0].index + 1);
    success = true;
    return;
  }
  double nvx = vx, nvy = vy;

  if ((int)ref.size() == 2)
    nvx *= -1, nvy *= -1;
  else
    nvx = nv.x, nvy = nv.y;

  Vector v(vx, vy);
  compute(remain - timeLimit, nvx, nvy, cur + v * timeLimit);
}

int main() {
  while (cin >> n, n) {
    double vx, vy;
    cin >> w >> h >> r >> vx >> vy;
    table[0] = Line(Point(0, 0), Point(w, 0));
    table[1] = Line(Point(w, 0), Point(w, h));
    table[2] = Line(Point(w, h), Point(0, h));
    table[3] = Line(Point(0, h), Point(0, 0));
    rep(i, n) cin >> ps[i].x >> ps[i].y;
    success = false;
    compute(10000, vx, vy, ps[0]);
    if (!success)
      puts("-1");
  }
  return 0;
}

Error: 0

Fixed submission:

#include <bits/stdc++.h>

#define REP(i, s, n) for (int i = s; i < n; i++)
#define rep(i, n) REP(i, 0, n)
#define EPS (1e-20)
#define equals(a, b) (fabs((a) - (b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

class Point {
public:
  double x, y;

  Point(double x = 0, double y = 0) : 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 a) { return Point(a * x, a * y); }
  Point operator/(double a) { return Point(x / a, y / a); }
  Point operator*(Point a) {
    return Point(x * a.x - y * a.y, x * a.y + y * a.x);
  }

  bool operator<(const Point &p) const {
    return !equals(x, p.x) ? x < p.x : (!equals(y, p.y) && y < p.y);
  }

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

struct Segment {
  Point p1, p2;
  Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
  bool operator<(const Segment &s) const {
    return (p2 == s.p2) ? p1 < s.p1 : p2 < s.p2;
  }
  bool operator==(const Segment &s) const {
    return (s.p1 == p1 && s.p2 == p2) || (s.p1 == p2 && s.p2 == p1);
  }
};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;

ostream &operator<<(ostream &os, const Point &a) {
  os << "(" << a.x << "," << a.y << ")";
}

ostream &operator<<(ostream &os, const Segment &a) {
  os << "( " << a.p1 << " , " << a.p2 << " )";
}

double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }

double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }

double norm(Point a) { return a.x * a.x + a.y * a.y; }

double abs(Point a) { return sqrt(norm(a)); }

// rad は角度をラジアンで持たせること
Point rotate(Point a, double rad) {
  return Point(cos(rad) * a.x - sin(rad) * a.y,
               sin(rad) * a.x + cos(rad) * a.y);
}

// 度をラジアンに変換
double toRad(double agl) { return agl * M_PI / 180.0; }

// a => prev, b => cur, c=> next
// prev から cur へ行って next へ行く際の角度を求める
double getArg(Point a, Point b, Point c) {
  double arg1 = atan2(b.y - a.y, b.x - a.x);
  double arg2 = atan2(c.y - b.y, c.x - b.x);
  double arg = fabs(arg1 - arg2);
  while (arg > M_PI)
    arg -= 2.0 * M_PI;
  return fabs(arg);
}

int ccw(Point p0, Point p1, Point p2) {
  Point a = p1 - p0;
  Point b = p2 - p0;
  if (cross(a, b) > EPS)
    return COUNTER_CLOCKWISE;
  if (cross(a, b) < -EPS)
    return CLOCKWISE;
  if (dot(a, b) < -EPS)
    return ONLINE_BACK;
  if (norm(a) < norm(b))
    return ONLINE_FRONT;
  return ON_SEGMENT;
}

bool intersectLL(Line l, Line m) {
  return abs(cross(l.p2 - l.p1, m.p2 - m.p1)) > EPS || // non-parallel
         abs(cross(l.p2 - l.p1, m.p1 - l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2 - l.p1, s.p1 - l.p1) * // s[0] is left of l
             cross(l.p2 - l.p1, s.p2 - l.p1) <
         EPS; // s[1] is right of l
}
bool intersectLP(Line l, Point p) {
  return abs(cross(l.p2 - p, l.p1 - p)) < EPS;
}
bool intersectSS(Line s, Line t) {
  return ccw(s.p1, s.p2, t.p1) * ccw(s.p1, s.p2, t.p2) <= 0 &&
         ccw(t.p1, t.p2, s.p1) * ccw(t.p1, t.p2, s.p2) <= 0;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1 - p) + abs(s.p2 - p) - abs(s.p2 - s.p1) <
         EPS; // triangle inequality
}

Point projection(Line l, Point p) {
  double t = dot(p - l.p1, l.p1 - l.p2) / norm(l.p1 - l.p2);
  return l.p1 + (l.p1 - l.p2) * t;
}
Point reflection(Line l, Point p) { return p + (projection(l, p) - p) * 2; }
double distanceLP(Line l, Point p) { return abs(p - projection(l, p)); }
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s))
    return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r))
    return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t))
    return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.p2)));
}

Point crosspoint(Line l, Line m) {
  double A = cross(l.p2 - l.p1, m.p2 - m.p1);
  double B = cross(l.p2 - l.p1, l.p2 - m.p1);
  if (abs(A) < EPS && abs(B) < EPS) {
    vector<Point> vec;
    vec.push_back(l.p1), vec.push_back(l.p2), vec.push_back(m.p1),
        vec.push_back(m.p2);
    sort(vec.begin(), vec.end());
    assert(vec[1] == vec[2]); // 同じセグメントかもよ
    return vec[1];
    // return m.p1;
  }
  if (abs(A) < EPS)
    assert(false);
  return m.p1 + (m.p2 - m.p1) * (B / A);
}

// cross product of pq and pr
double cross3p(Point p, Point q, Point r) {
  return (r.x - q.x) * (p.y - q.y) - (r.y - q.y) * (p.x - q.x);
}

// returns true if point r is on the same line as the line pq
bool collinear(Point p, Point q, Point r) {
  return fabs(cross3p(p, q, r)) < EPS;
}

// returns true if point t is on the left side of line pq
bool ccwtest(Point p, Point q, Point r) {
  return cross3p(p, q, r) > 0; // can be modified to accept collinear points
}

bool onSegment(Point p, Point q, Point r) {
  return collinear(p, q, r) &&
         equals(sqrt(pow(p.x - r.x, 2) + pow(p.y - r.y, 2)) +
                    sqrt(pow(r.x - q.x, 2) + pow(r.y - q.y, 2)),
                sqrt(pow(p.x - q.x, 2) + pow(p.y - q.y, 2)));
}

bool isConvex(vector<Point> p) {
  int sz = (int)p.size();
  if (sz < 3)
    return false; // boundary case, we treat a point or a line as not convex
  bool isLeft = ccwtest(p[0], p[1], p[2]);
  for (int i = 1; i < (int)p.size(); i++)
    if (ccwtest(p[i], p[(i + 1) % sz], p[(i + 2) % sz]) != isLeft)
      return false;
  return true;
}

double angle(Point a, Point b, Point c) {
  double ux = b.x - a.x, uy = b.y - a.y;
  double vx = c.x - a.x, vy = c.y - a.y;
  return acos((ux * vx + uy * vy) /
              sqrt((ux * ux + uy * uy) * (vx * vx + vy * vy)));
}

// 多角形poly内（線分上も含む）に点pが存在するかどうは判定する
bool inPolygon(Polygon poly, Point p) {
  if ((int)poly.size() == 0)
    return false;
  rep(i, poly.size()) if (onSegment(poly[i], poly[(i + 1) % poly.size()],
                                    p)) return true;
  double sum = 0;
  for (int i = 0; i < (int)poly.size(); i++) {
    if (equals(cross(poly[i] - p, poly[(i + 1) % poly.size()] - p), 0.0))
      continue; // ３点が平行だとangleがnanを返しsumがnanになり死ぬ
    if (cross3p(p, poly[i], poly[(i + 1) % poly.size()]) < 0)
      sum -= angle(p, poly[i], poly[(i + 1) % poly.size()]);
    else
      sum += angle(p, poly[i], poly[(i + 1) % poly.size()]);
  }
  // あまり誤差を厳しくしすぎると良くないので以下のほうが良い
  const double eps = 1e-5;
  return (fabs(sum - 2 * M_PI) < eps || fabs(sum + 2 * M_PI) < eps);
}

typedef pair<double, double> dd;
const double DINF = 1e20;
bool LT(double a, double b) { return !equals(a, b) && a < b; }
bool LTE(double a, double b) { return equals(a, b) || a < b; }
#define pow2(a) ((a) * (a))

dd calc(double x1, double y1, double vx1, double vy1, double x2, double y2,
        double vx2, double vy2, double r) {
  double VX = (vx1 - vx2), X = (x1 - x2), VY = (vy1 - vy2), Y = (y1 - y2);
  double a = pow2(VX) + pow2(VY), b = 2 * (X * VX + Y * VY),
         c = pow2(X) + pow2(Y) - pow2(r);
  dd ret = dd(DINF, DINF);
  double D = b * b - 4 * a * c;

  if (LT(D, 0.0))
    return ret;

  if (equals(a, 0.0)) {
    if (equals(b, 0.0))
      return ret;
    if (LT(-c / b, 0.0))
      return ret;
    ret.first = -c / b;
    return ret;
  }

  if (equals(D, 0.0))
    D = 0;
  ret.first = (-b - sqrt(D)) / (2 * a);
  ret.second = (-b + sqrt(D)) / (2 * a);
  if (!equals(ret.first, ret.second) && ret.first > ret.second)
    swap(ret.first, ret.second);
  return ret;
}

const int MAX_N = 20;
const double TIME = 100000;
int n;
double w, h, r;
Point ps[MAX_N];
Line table[4];
Vector es[4] = {Vector(100, 0), Vector(0, 100), Vector(-100, 0),
                Vector(0, -100)};

typedef pair<double, int> di;
bool COMP(const di &a, const di &b) {
  if (!equals(a.first, b.first))
    return LT(a.first, b.first);
  return a.second < b.second;
}

bool success = false;

struct Data {
  int index;
  double time;

  Point rp, cp2;
  bool operator<(const Data &data) const {
    if (!equals(time, data.time))
      return LT(time, data.time);
    if (index != data.index)
      return index < data.index;
    if (!(rp == data.rp))
      return rp < data.rp;
    return cp2 < data.cp2;
  }
};

vector<Data> getReflection(double remain, double vx, double vy, Point cur,
                           Vector &nv) {
  vector<Data> ret, temp;
  Vector v = Vector(vx, vy);
  rep(i, 4) {
    Vector h = es[i] * Vector(0, 1);
    Line line = Line(cur, cur + h);
    Point cp = crosspoint(table[i], line);
    Vector e = (cp - cur) / abs(cp - cur);
    Point ep = cur + e * r;
    Segment seg = Segment(ep, ep + v * TIME);

    if (intersectLS(table[i], seg)) {
      Point cp2 = crosspoint(table[i], seg);
      double timer = abs(cp2 - ep) / abs(v);
      if (equals(timer, 0.0))
        continue;

      Line wall = Line(cp2, cp2 + h);
      Point rp = reflection(wall, ep);
      temp.push_back((Data){i, timer, rp, cp2});

      /*
      Line wall = Line(cp2,cp2+h);
      Point rep = reflection(wall,ep);
      nv = ( rep - cp2 ) / abs( rep - cp2 );
      */
    }
  }
  if (!temp.empty()) {
    sort(temp.begin(), temp.end());
    double mini = temp[0].time;
    if (LT(remain, mini)) {
      mini = remain;
      ret.push_back((Data){-1, mini});
    }
    rep(i, temp.size()) if (equals(mini, temp[i].time)) {
      ret.push_back(temp[i]);
      nv = (temp[i].rp - temp[i].cp2) / abs(temp[i].rp - temp[i].cp2);
    }
  }
  return ret;
}

void compute(double remain, double vx, double vy, Point cur) {
  if (equals(remain, 0))
    return;
  // cout << "remain = " << remain << " v (" << vx << "," << vy << ") ; cp = "
  // << cur  << endl;
  Vector nv = Vector(123, 456);
  vector<Data> ref = getReflection(remain, vx, vy, cur, nv);
  assert(1 <= ref.size() && ref.size() <= 2);
  double timeLimit = ref[0].time;
  // cout << "ref.size() = " << ref.size() << " " << nv << endl;
  // cout << "timeLimit = " << timeLimit  << " => " <<
  // cur+Vector(vx,vy)*timeLimit<< endl;
  vector<Data> collides;
  REP(i, 1, n) {
    dd temp = calc(cur.x, cur.y, vx, vy, ps[i].x, ps[i].y, 0, 0, 2 * r);
    vector<double> vec;
    vec.push_back(temp.first), vec.push_back(temp.second);
    double mini = DINF;
    rep(j, vec.size()) if (LTE(0.0, vec[j]) && LTE(vec[j], timeLimit)) mini =
        min(mini, vec[j], LT);
    if (!equals(mini, DINF))
      collides.push_back((Data){i, mini});
    // cout << "ball " << i << " : " << temp.first << "," << temp.second <<
    // endl;
  }
  if (!collides.empty()) {
    sort(collides.begin(), collides.end());
    printf("%d\\n", collides[0].index + 1);
    success = true;
    return;
  }
  double nvx = vx, nvy = vy;
  if ((int)ref.size() == 2)
    nvx *= -1, nvy *= -1;
  else
    nvx = nv.x, nvy = nv.y;
  Vector v(vx, vy);
  compute(remain - timeLimit, nvx, nvy, cur + v * timeLimit);
}

int main() {
  while (cin >> n, n) {
    double vx, vy;
    cin >> w >> h >> r >> vx >> vy;
    table[0] = Line(Point(0, 0), Point(w, 0));
    table[1] = Line(Point(w, 0), Point(w, h));
    table[2] = Line(Point(w, h), Point(0, h));
    table[3] = Line(Point(0, h), Point(0, 0));
    rep(i, n) cin >> ps[i].x >> ps[i].y;
    success = false;
    compute(10000, vx, vy, ps[0]);
    if (!success)
      puts("-1");
  }
  return 0;
}