Problem p01297 (C++) — buggy submission, verdict: Time Limit Exceeded

////////////////////////////////////////
///  tu3 pro-con template            ///
////////////////////////////////////////
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstring>
#include <functional>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;

//// MACRO ////
#define countof(a) (sizeof(a) / sizeof(a[0]))

#define REP(i, n) for (int i = 0; i < (n); i++)
#define RREP(i, n) for (int i = (n)-1; i >= 0; i--)
#define FOR(i, s, n) for (int i = (s); i < (n); i++)
#define RFOR(i, s, n) for (int i = (n)-1; i >= (s); i--)
#define pos(c, i) c.being() + (i)
#define allof(c) c.begin(), c.end()
#define aallof(a) a, countof(a)
#define partof(c, i, n) c.begin() + (i), c.begin() + (i) + (n)
#define apartof(a, i, n) a + (i), a + (i) + (n)
#define long long long

#define EPS 1e-9
#define INF (1L << 30)
#define LINF (1LL << 60)

#define PREDICATE(t, a, exp) [&](const t &a) -> bool { return exp; }
#define COMPARISON_T(t) bool (*)(const t &, const t &)
#define COMPARISON(t, a, b, exp)                                               \\
  [&](const t &a, const t &b) -> bool { return exp; }
#define CONVERTER(TSrc, t, TDest, exp)                                         \\
  [&](const TSrc &t) -> TDest { return exp; }

inline int sign(double x) { return (abs(x) < EPS ? 0 : x > 0 ? 1 : -1); }

//// i/o helper ////

struct _Reader {
  template <class T> _Reader operator,(T &rhs) {
    cin >> rhs;
    return *this;
  }
};
struct _Writer {
  bool f;
  _Writer() : f(false) {}
  template <class T> _Writer operator,(const T &rhs) {
    cout << (f ? " " : "") << rhs;
    f = true;
    return *this;
  }
};
#define READ(t, ...)                                                           \\
  t __VA_ARGS__;                                                               \\
  _Reader(), __VA_ARGS__
#define WRITE(...)                                                             \\
  _Writer(), __VA_ARGS__;                                                      \\
  cout << endl

template <class T> struct vevector : public vector<vector<T>> {
  vevector(int n = 0, int m = 0, const T &initial = T())
      : vector<vector<T>>(n, vector<T>(m, initial)) {}
};
template <class T> struct vevevector : public vector<vevector<T>> {
  vevevector(int n = 0, int m = 0, int l = 0, const T &initial = T())
      : vector<vevector<T>>(n, vevector<T>(m, l, initial)) {}
};
template <class T> struct vevevevector : public vector<vevevector<T>> {
  vevevevector(int n = 0, int m = 0, int l = 0, int k = 0,
               const T &initial = T())
      : vector<vevevector<T>>(n, vevevector<T>(m, l, k, initial)) {}
};
template <class T> T read() {
  T t;
  cin >> t;
  return t;
}
template <class T> vector<T> read(int n) {
  vector<T> v;
  REP(i, n) { v.push_back(read<T>()); }
  return v;
}
template <class T> vevector<T> read(int n, int m) {
  vevector<T> v;
  REP(i, n) v.push_back(read<T>(m));
  return v;
}
template <class T> vevector<T> readjag() { return read<T>(read<int>()); }
template <class T> vevector<T> readjag(int n) {
  vevector<T> v;
  REP(i, n) v.push_back(readjag<T>());
  return v;
}

template <class T1, class T2>
inline istream &operator>>(istream &in, pair<T1, T2> &p) {
  in >> p.first >> p.second;
  return in;
}
template <class T1, class T2>
inline ostream &operator<<(ostream &out, pair<T1, T2> &p) {
  out << p.first << p.second;
  return out;
}
template <class T> inline ostream &operator<<(ostream &out, vector<T> &v) {
  ostringstream ss;
  for (auto x : v)
    ss << x << ' ';
  auto s = ss.str();
  out << s.substr(0, s.length() - 1) << endl;
  return out;
}

/// 2次元
struct P2 {
  double x, y;
  P2(double x = 0, double y = 0) : x(x), y(y) {}
  P2(complex<double> c) : x(c.real()), y(c.imag()) {}
  P2 operator+() const { return *this; }
  P2 operator+(const P2 &_) const { return P2(x + _.x, y + _.y); }
  P2 operator-() const { return P2(-x, -y); }
  P2 operator-(const P2 &_) const { return *this + -_; }
  P2 operator*(double _) const { return P2(x * _, y * _); }
  P2 operator/(double _) const { return P2(x / _, y / _); }
  double dot(const P2 &_) const { return x * _.x + y * _.y; }   // 内積
  double cross(const P2 &_) const { return x * _.y - y * _.x; } // 外積
  double sqlength() const { return x * x + y * y; }             // 二乗長さ
  double length() const { return sqrt(sqlength()); }            // 長さ
  P2 orthogonal() const { return P2(y, -x); }
  P2 direction() const { return *this / length(); } // 方向ベクトル
};
inline istream &operator>>(istream &in, P2 &p) {
  in >> p.x >> p.y;
  return in;
}
inline ostream &operator<<(ostream &out, const P2 &p) {
  out << p.x << ' ' << p.y;
  return out;
}
inline double abs(P2 p2) { return p2.length(); }
inline P2 orthogonal(P2 p) { return p.orthogonal(); }
inline complex<double> orthogonal(complex<double> c) {
  return c * complex<double>(0, 1);
}

// a,b から ちょうど d だけ離れた点。aとbを円周に持つ円の半径。
inline pair<P2, P2> get_same_distance_points(P2 a, P2 b, double d) {
  assert(abs(a - b) <= 2 * d + EPS);
  auto v = (a + b) / 2.0 - a; // a から aとbの中点
  auto vl = abs(v);
  auto wl = sqrt(d * d - vl * vl);    // 直行Vの大きさ
  auto w = orthogonal(v) * (wl / vl); // 直行V
  return make_pair(a + v + w, a + v - w);
}

// a から b に向かって、cが右手か左手か。
inline int clockwise(P2 a, P2 b, P2 c) {
  const P2 u = b - a, v = c - a;
  if (u.cross(v) > EPS) {
    return 1;
  }
  if (u.cross(v) < -EPS) {
    return -1;
  }
  if (u.dot(v) < -EPS) {
    return -1;
  }
  if (u.sqlength() < v.sqlength() - EPS) {
    return 1;
  }
  return 0;
}

/// 直線
struct Line {
  P2 p, d;
  explicit Line(P2 pos = P2(), P2 dir = P2()) : p(pos), d(dir) {}
  static Line FromPD(P2 pos, P2 dir) { return Line(pos, dir); }
  static Line From2Point(P2 a, P2 b) { return Line(a, b - a); }
};

/// 線分
struct LineSeg {
  P2 p, d;
  explicit LineSeg(P2 pos = P2(), P2 dir = P2()) : p(pos), d(dir) {}
  static LineSeg FromPD(P2 pos, P2 dir) { return LineSeg(pos, dir); }
  static LineSeg From2Point(P2 a, P2 b) { return LineSeg(a, b - a); }
  operator Line() { return Line(p, d); }
};

inline P2 projective(P2 a, P2 b) { return a * (a.dot(b) / a.length()); }
inline P2 perpendicular_foot(P2 a, Line b) {
  Line l = Line(b.p - a, b.d);
  return a + l.p - projective(l.p, l.d);
}
inline LineSeg projective(LineSeg a, Line b) {
  return LineSeg(perpendicular_foot(a.p, b), projective(a.d, b.d));
}

// 交点
inline P2 crossPoint(Line a, Line b) {
  return a.p + a.d * (b.d.cross(b.p - a.p) / b.d.cross(a.d));
}

// 包括判定
inline bool contains(LineSeg a, P2 p) {
  return abs(a.p - p) + abs(a.p + a.d - p) - abs(a.d) < EPS;
}

// 交差判定
inline bool isCross(Line a, Line b) { return abs(a.d.cross(b.d)) > EPS; }
inline bool isCross(Line a, LineSeg b) {
  return sign(a.d.cross(b.p - a.p)) * sign(a.d.cross(b.p + b.d - a.d)) <= 0;
}
inline bool isCross(LineSeg a, Line b) { return isCross(b, a); }
inline bool isCross(LineSeg a, LineSeg b) {
  P2 ae = a.p + a.d, be = b.p + b.d;
  return clockwise(a.p, ae, b.p) * clockwise(a.p, ae, be) <= 0 &&
         clockwise(b.p, be, a.p) * clockwise(b.p, be, ae) <= 0;
}

// 重なり判定
inline bool isOverlap(Line a, Line b) {
  return abs(a.d.cross(b.p - a.p)) < EPS;
}
inline bool isOverlap(Line a, LineSeg b) {
  return isOverlap(a, Line(b.p, b.d));
}
inline bool isOverlap(LineSeg a, Line b) { return isOverlap(b, a); }
inline bool isOverlap(LineSeg a, LineSeg b) {
  return contains(a, b.p) || contains(a, b.p + b.d) || contains(b, a.p) ||
         contains(b, a.p + a.d);
}

// 距離
inline double getDistance(P2 a, P2 b) { return (a - b).length(); }
inline double getDistance(P2 a, Line b) {
  return abs(b.d.cross(a - b.p) / b.d.length());
}
inline double getDistance(P2 a, LineSeg b) {
  return min(getDistance(perpendicular_foot(a, (Line)b), a),
             min(getDistance(b.p, a), getDistance(b.p + b.d, a)));
}
inline double getDistance(Line a, P2 b) { return getDistance(b, a); }
inline double getDistance(Line a, Line b) {
  return isCross(a, b) ? 0 : getDistance(a, b.p);
}
inline double getDistance(Line a, LineSeg b) {
  return isCross(a, b) ? 0
                       : min(getDistance(a, b.p), getDistance(a, b.p + b.d));
}
inline double getDistance(LineSeg a, P2 b) { return getDistance(b, a); }
inline double getDistance(LineSeg a, Line b) { return getDistance(b, a); }
inline double getDistance(LineSeg a, LineSeg b) {
  return isCross(a, b)
             ? 0
             : min(min(getDistance(a.p, b.p), getDistance(a.p, b.p + b.d)),
                   min(getDistance(a.p + a.d, b.p),
                       getDistance(a.p + a.d, b.p + b.d)));
}

// a から ta, bから tb だけ離れた点。ta=tb=r なら aとbに内接する円
inline pair<pair<P2, P2>, pair<P2, P2>> get_distance_points(Line a, double ta,
                                                            Line b, double tb) {
  assert(isCross(a, b));

  P2 va = a.d.orthogonal().direction() * ta;
  P2 vb = b.d.orthogonal().direction() * tb;
  return make_pair(
      make_pair(crossPoint(Line(a.p + va, a.d), Line(b.p + vb, b.d)),
                crossPoint(Line(a.p + va, a.d), Line(b.p - vb, b.d))),
      make_pair(crossPoint(Line(a.p - va, a.d), Line(b.p + vb, b.d)),
                crossPoint(Line(a.p - va, a.d), Line(b.p - vb, b.d))));
}

/// 円
struct Circle {
  P2 c;
  double r;
  Circle() : c(), r() {}
  Circle(double x, double y, double r) : c(x, y), r(r) {}
  Circle(P2 c, double r) : c(c), r(r) {}
  bool IntersectWith(const Circle &rhs) const {
    return abs(c - rhs.c) - (r + rhs.r) < EPS;
  } // 接してても真。
  bool Contains(const P2 &p) const {
    return abs(p - c) - r < EPS;
  } // 接してても真。
};
inline istream &operator>>(istream &in, Circle &c) {
  in >> c.c >> c.r;
  return in;
}

// 交差している2円の交点を求める。角度の小さい方から出る(右下方向が正なら時計回り)
inline pair<P2, P2> crossPoint(Circle A, Circle B) {
  P2 v = B.c - A.c;
  P2 dir = v.direction(); // 他方の中心への方向
  double d = v.length();  // 他方の中心への距離
  double lh = (A.r * A.r + d * d - B.r * B.r) / (2 * d); // 垂線の足までの距離
  P2 h = A.c + dir * lh;                                 // 垂線の足
  double lp = sqrt(A.r * A.r - lh * lh); // 垂線の足から交点までの距離
  P2 p = dir.orthogonal() * lp;   // 垂線の足から交点へのベクトル
  return make_pair(h + p, h - p); // 交点の組。
}

/// 長方形
struct Rect {
  P2 l, s;
  Rect() : l(), s() {}
  Rect(double x, double y, double w, double h) : l(x, y), s(w, h) {}
  Rect(P2 location, P2 size) : l(location), s(size) {}
  bool Contains(const P2 &p) const {
    return p.x - l.x > -EPS && p.y - l.y > -EPS && p.x - (l.x + s.x) < EPS &&
           p.y - (l.y + s.y) < EPS;
  } // 接してても真。
};

//// start up ////
void solve();
int main() {
  solve();
  return 0;
}

////////////////////
/// template end ///
////////////////////

void solve() {
  int cases = INF;
  REP(_, cases) {
    READ(int, W, H, N, R);
    if (!W) {
      break;
    }

    struct Laser {
      Line line;
      double thick;
    };
    vector<Laser> beams;
    REP(i, N) {
      READ(double, x, y, z, w, t);
      beams.push_back({Line::From2Point(P2(x, y), P2(z, w)), t});
    }

    // 画面端も死ぬ
    beams.push_back({Line::From2Point(P2(0, 0), P2(W, 0)), 0});
    beams.push_back({Line::From2Point(P2(W, 0), P2(W, H)), 0});
    beams.push_back({Line::From2Point(P2(W, H), P2(0, H)), 0});
    beams.push_back({Line::From2Point(P2(0, H), P2(0, 0)), 0});

    // 移動可能範囲
    Rect screen(R, R, W - R, H - R);

    bool ok = false;
    for (auto i : beams)
      for (auto j : beams) {
        // WRITE("i:", i.line.p, i.thick, "j:", j.line.p, j.thick);
        if (isCross(i.line, j.line)) {
          // 点の候補
          auto cand =
              get_distance_points(i.line, i.thick + R, j.line, j.thick + R);
          P2 ps[] = {
              cand.first.first,
              cand.first.second,
              cand.second.first,
              cand.second.second,
          };

          for (auto p : ps) {

            // その位置は、移動可能でかつすべてのレーザーに当たらない？
            bool test = true;
            test &= screen.Contains(p);
            if (!test)
              continue;

            // WRITE(p);
            for (auto k : beams) {
              // WRITE("k:", k.line.p, k.thick,
              //	"distance:", getDistance(k.line, p),
              //	"need:", (k.thick + R),
              //	"is ok? ", (getDistance(k.line, p) - (k.thick + R) >
              //-EPS));
              test &= (getDistance(k.line, p) - (k.thick + R) > -EPS);
            }
            ok |= test;
            // WRITE(p, "ok? ", ok);
            if (ok)
              break;
          }
        } else {
          // 平行……。今回は画面端があるので、平行は考えなくてよい。
        }
      }

    WRITE(ok ? "Yes" : "No");
  }
}

Error: TLE

Fixed submission:

////////////////////////////////////////
///  tu3 pro-con template            ///
////////////////////////////////////////
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstring>
#include <functional>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;

//// MACRO ////
#define countof(a) (sizeof(a) / sizeof(a[0]))

#define REP(i, n) for (int i = 0; i < (n); i++)
#define RREP(i, n) for (int i = (n)-1; i >= 0; i--)
#define FOR(i, s, n) for (int i = (s); i < (n); i++)
#define RFOR(i, s, n) for (int i = (n)-1; i >= (s); i--)
#define pos(c, i) c.being() + (i)
#define allof(c) c.begin(), c.end()
#define aallof(a) a, countof(a)
#define partof(c, i, n) c.begin() + (i), c.begin() + (i) + (n)
#define apartof(a, i, n) a + (i), a + (i) + (n)
#define long long long

#define EPS 1e-9
#define INF (1L << 30)
#define LINF (1LL << 60)

#define PREDICATE(t, a, exp) [&](const t &a) -> bool { return exp; }
#define COMPARISON_T(t) bool (*)(const t &, const t &)
#define COMPARISON(t, a, b, exp)                                               \\
  [&](const t &a, const t &b) -> bool { return exp; }
#define CONVERTER(TSrc, t, TDest, exp)                                         \\
  [&](const TSrc &t) -> TDest { return exp; }

inline int sign(double x) { return (abs(x) < EPS ? 0 : x > 0 ? 1 : -1); }

//// i/o helper ////

struct _Reader {
  template <class T> _Reader operator,(T &rhs) {
    cin >> rhs;
    return *this;
  }
};
struct _Writer {
  bool f;
  _Writer() : f(false) {}
  template <class T> _Writer operator,(const T &rhs) {
    cout << (f ? " " : "") << rhs;
    f = true;
    return *this;
  }
};
#define READ(t, ...)                                                           \\
  t __VA_ARGS__;                                                               \\
  _Reader(), __VA_ARGS__
#define WRITE(...)                                                             \\
  _Writer(), __VA_ARGS__;                                                      \\
  cout << endl

template <class T> struct vevector : public vector<vector<T>> {
  vevector(int n = 0, int m = 0, const T &initial = T())
      : vector<vector<T>>(n, vector<T>(m, initial)) {}
};
template <class T> struct vevevector : public vector<vevector<T>> {
  vevevector(int n = 0, int m = 0, int l = 0, const T &initial = T())
      : vector<vevector<T>>(n, vevector<T>(m, l, initial)) {}
};
template <class T> struct vevevevector : public vector<vevevector<T>> {
  vevevevector(int n = 0, int m = 0, int l = 0, int k = 0,
               const T &initial = T())
      : vector<vevevector<T>>(n, vevevector<T>(m, l, k, initial)) {}
};
template <class T> T read() {
  T t;
  cin >> t;
  return t;
}
template <class T> vector<T> read(int n) {
  vector<T> v;
  REP(i, n) { v.push_back(read<T>()); }
  return v;
}
template <class T> vevector<T> read(int n, int m) {
  vevector<T> v;
  REP(i, n) v.push_back(read<T>(m));
  return v;
}
template <class T> vevector<T> readjag() { return read<T>(read<int>()); }
template <class T> vevector<T> readjag(int n) {
  vevector<T> v;
  REP(i, n) v.push_back(readjag<T>());
  return v;
}

template <class T1, class T2>
inline istream &operator>>(istream &in, pair<T1, T2> &p) {
  in >> p.first >> p.second;
  return in;
}
template <class T1, class T2>
inline ostream &operator<<(ostream &out, pair<T1, T2> &p) {
  out << p.first << p.second;
  return out;
}
template <class T> inline ostream &operator<<(ostream &out, vector<T> &v) {
  ostringstream ss;
  for (auto x : v)
    ss << x << ' ';
  auto s = ss.str();
  out << s.substr(0, s.length() - 1) << endl;
  return out;
}

/// 2次元
struct P2 {
  double x, y;
  P2(double x = 0, double y = 0) : x(x), y(y) {}
  P2(complex<double> c) : x(c.real()), y(c.imag()) {}
  P2 operator+() const { return *this; }
  P2 operator+(const P2 &_) const { return P2(x + _.x, y + _.y); }
  P2 operator-() const { return P2(-x, -y); }
  P2 operator-(const P2 &_) const { return *this + -_; }
  P2 operator*(double _) const { return P2(x * _, y * _); }
  P2 operator/(double _) const { return P2(x / _, y / _); }
  double dot(const P2 &_) const { return x * _.x + y * _.y; }   // 内積
  double cross(const P2 &_) const { return x * _.y - y * _.x; } // 外積
  double sqlength() const { return x * x + y * y; }             // 二乗長さ
  double length() const { return sqrt(sqlength()); }            // 長さ
  P2 orthogonal() const { return P2(y, -x); }
  P2 direction() const { return *this / length(); } // 方向ベクトル
};
inline istream &operator>>(istream &in, P2 &p) {
  in >> p.x >> p.y;
  return in;
}
inline ostream &operator<<(ostream &out, const P2 &p) {
  out << p.x << ' ' << p.y;
  return out;
}
inline double abs(P2 p2) { return p2.length(); }
inline P2 orthogonal(P2 p) { return p.orthogonal(); }
inline complex<double> orthogonal(complex<double> c) {
  return c * complex<double>(0, 1);
}

// a,b から ちょうど d だけ離れた点。aとbを円周に持つ円の半径。
inline pair<P2, P2> get_same_distance_points(P2 a, P2 b, double d) {
  assert(abs(a - b) <= 2 * d + EPS);
  auto v = (a + b) / 2.0 - a; // a から aとbの中点
  auto vl = abs(v);
  auto wl = sqrt(d * d - vl * vl);    // 直行Vの大きさ
  auto w = orthogonal(v) * (wl / vl); // 直行V
  return make_pair(a + v + w, a + v - w);
}

// a から b に向かって、cが右手か左手か。
inline int clockwise(P2 a, P2 b, P2 c) {
  const P2 u = b - a, v = c - a;
  if (u.cross(v) > EPS) {
    return 1;
  }
  if (u.cross(v) < -EPS) {
    return -1;
  }
  if (u.dot(v) < -EPS) {
    return -1;
  }
  if (u.sqlength() < v.sqlength() - EPS) {
    return 1;
  }
  return 0;
}

/// 直線
struct Line {
  P2 p, d;
  explicit Line(P2 pos = P2(), P2 dir = P2()) : p(pos), d(dir) {}
  static Line FromPD(P2 pos, P2 dir) { return Line(pos, dir); }
  static Line From2Point(P2 a, P2 b) { return Line(a, b - a); }
};

/// 線分
struct LineSeg {
  P2 p, d;
  explicit LineSeg(P2 pos = P2(), P2 dir = P2()) : p(pos), d(dir) {}
  static LineSeg FromPD(P2 pos, P2 dir) { return LineSeg(pos, dir); }
  static LineSeg From2Point(P2 a, P2 b) { return LineSeg(a, b - a); }
  operator Line() { return Line(p, d); }
};

inline P2 projective(P2 a, P2 b) { return a * (a.dot(b) / a.length()); }
inline P2 perpendicular_foot(P2 a, Line b) {
  Line l = Line(b.p - a, b.d);
  return a + l.p - projective(l.p, l.d);
}
inline LineSeg projective(LineSeg a, Line b) {
  return LineSeg(perpendicular_foot(a.p, b), projective(a.d, b.d));
}

// 交点
inline P2 crossPoint(Line a, Line b) {
  return a.p + a.d * (b.d.cross(b.p - a.p) / b.d.cross(a.d));
}

// 包括判定
inline bool contains(LineSeg a, P2 p) {
  return abs(a.p - p) + abs(a.p + a.d - p) - abs(a.d) < EPS;
}

// 交差判定
inline bool isCross(Line a, Line b) { return abs(a.d.cross(b.d)) > EPS; }
inline bool isCross(Line a, LineSeg b) {
  return sign(a.d.cross(b.p - a.p)) * sign(a.d.cross(b.p + b.d - a.d)) <= 0;
}
inline bool isCross(LineSeg a, Line b) { return isCross(b, a); }
inline bool isCross(LineSeg a, LineSeg b) {
  P2 ae = a.p + a.d, be = b.p + b.d;
  return clockwise(a.p, ae, b.p) * clockwise(a.p, ae, be) <= 0 &&
         clockwise(b.p, be, a.p) * clockwise(b.p, be, ae) <= 0;
}

// 重なり判定
inline bool isOverlap(Line a, Line b) {
  return abs(a.d.cross(b.p - a.p)) < EPS;
}
inline bool isOverlap(Line a, LineSeg b) {
  return isOverlap(a, Line(b.p, b.d));
}
inline bool isOverlap(LineSeg a, Line b) { return isOverlap(b, a); }
inline bool isOverlap(LineSeg a, LineSeg b) {
  return contains(a, b.p) || contains(a, b.p + b.d) || contains(b, a.p) ||
         contains(b, a.p + a.d);
}

// 距離
inline double getDistance(P2 a, P2 b) { return (a - b).length(); }
inline double getDistance(P2 a, Line b) {
  return abs(b.d.cross(a - b.p) / b.d.length());
}
inline double getDistance(P2 a, LineSeg b) {
  return min(getDistance(perpendicular_foot(a, (Line)b), a),
             min(getDistance(b.p, a), getDistance(b.p + b.d, a)));
}
inline double getDistance(Line a, P2 b) { return getDistance(b, a); }
inline double getDistance(Line a, Line b) {
  return isCross(a, b) ? 0 : getDistance(a, b.p);
}
inline double getDistance(Line a, LineSeg b) {
  return isCross(a, b) ? 0
                       : min(getDistance(a, b.p), getDistance(a, b.p + b.d));
}
inline double getDistance(LineSeg a, P2 b) { return getDistance(b, a); }
inline double getDistance(LineSeg a, Line b) { return getDistance(b, a); }
inline double getDistance(LineSeg a, LineSeg b) {
  return isCross(a, b)
             ? 0
             : min(min(getDistance(a.p, b.p), getDistance(a.p, b.p + b.d)),
                   min(getDistance(a.p + a.d, b.p),
                       getDistance(a.p + a.d, b.p + b.d)));
}

// a から ta, bから tb だけ離れた点。ta=tb=r なら aとbに内接する円
inline pair<pair<P2, P2>, pair<P2, P2>> get_distance_points(Line a, double ta,
                                                            Line b, double tb) {
  assert(isCross(a, b));

  P2 va = a.d.orthogonal().direction() * ta;
  P2 vb = b.d.orthogonal().direction() * tb;
  return make_pair(
      make_pair(crossPoint(Line(a.p + va, a.d), Line(b.p + vb, b.d)),
                crossPoint(Line(a.p + va, a.d), Line(b.p - vb, b.d))),
      make_pair(crossPoint(Line(a.p - va, a.d), Line(b.p + vb, b.d)),
                crossPoint(Line(a.p - va, a.d), Line(b.p - vb, b.d))));
}

/// 円
struct Circle {
  P2 c;
  double r;
  Circle() : c(), r() {}
  Circle(double x, double y, double r) : c(x, y), r(r) {}
  Circle(P2 c, double r) : c(c), r(r) {}
  bool IntersectWith(const Circle &rhs) const {
    return abs(c - rhs.c) - (r + rhs.r) < EPS;
  } // 接してても真。
  bool Contains(const P2 &p) const {
    return abs(p - c) - r < EPS;
  } // 接してても真。
};
inline istream &operator>>(istream &in, Circle &c) {
  in >> c.c >> c.r;
  return in;
}

// 交差している2円の交点を求める。角度の小さい方から出る(右下方向が正なら時計回り)
inline pair<P2, P2> crossPoint(Circle A, Circle B) {
  P2 v = B.c - A.c;
  P2 dir = v.direction(); // 他方の中心への方向
  double d = v.length();  // 他方の中心への距離
  double lh = (A.r * A.r + d * d - B.r * B.r) / (2 * d); // 垂線の足までの距離
  P2 h = A.c + dir * lh;                                 // 垂線の足
  double lp = sqrt(A.r * A.r - lh * lh); // 垂線の足から交点までの距離
  P2 p = dir.orthogonal() * lp;   // 垂線の足から交点へのベクトル
  return make_pair(h + p, h - p); // 交点の組。
}

/// 長方形
struct Rect {
  P2 l, s;
  Rect() : l(), s() {}
  Rect(double x, double y, double w, double h) : l(x, y), s(w, h) {}
  Rect(P2 location, P2 size) : l(location), s(size) {}
  bool Contains(const P2 &p) const {
    return p.x - l.x > -EPS && p.y - l.y > -EPS && p.x - (l.x + s.x) < EPS &&
           p.y - (l.y + s.y) < EPS;
  } // 接してても真。
};

//// start up ////
void solve();
int main() {
  freopen("E:/My Documents/Downloads/regional-2009-data/E.txt", "r", stdin);
  freopen("E:/My Documents/Downloads/regional-2009-data/E.out.txt", "w",
          stdout);

  solve();
  return 0;
}

////////////////////
/// template end ///
////////////////////

void solve() {
  int cases = INF;
  REP(_, cases) {
    READ(int, W, H, N, R);
    if (!W) {
      break;
    }

    struct Laser {
      Line line;
      double thick;
    };
    vector<Laser> beams;
    REP(i, N) {
      READ(double, x, y, z, w, t);
      beams.push_back({Line::From2Point(P2(x, y), P2(z, w)), t});
    }

    // 画面端も死ぬ
    beams.push_back({Line::From2Point(P2(0, 0), P2(W, 0)), 0});
    beams.push_back({Line::From2Point(P2(W, 0), P2(W, H)), 0});
    beams.push_back({Line::From2Point(P2(W, H), P2(0, H)), 0});
    beams.push_back({Line::From2Point(P2(0, H), P2(0, 0)), 0});

    // 移動可能範囲
    Rect screen(R, R, W - R, H - R);

    bool ok = false;
    for (auto i : beams)
      for (auto j : beams) {
        // WRITE("i:", i.line.p, i.thick, "j:", j.line.p, j.thick);
        if (isCross(i.line, j.line)) {
          // 点の候補
          auto cand =
              get_distance_points(i.line, i.thick + R, j.line, j.thick + R);
          P2 ps[] = {
              cand.first.first,
              cand.first.second,
              cand.second.first,
              cand.second.second,
          };

          for (auto p : ps) {

            // その位置は、移動可能でかつすべてのレーザーに当たらない？
            bool test = true;
            test &= screen.Contains(p);
            if (!test)
              continue;

            // WRITE(p);
            for (auto k : beams) {
              // WRITE("k:", k.line.p, k.thick,
              //	"distance:", getDistance(k.line, p),
              //	"need:", (k.thick + R),
              //	"is ok? ", (getDistance(k.line, p) - (k.thick + R) >
              //-EPS));
              test &= (getDistance(k.line, p) - (k.thick + R) > -EPS);
            }
            ok |= test;
            // WRITE(p, "ok? ", ok);
            if (ok)
              break;
          }
        } else {
          // 平行……。今回は画面端があるので、平行は考えなくてよい。
        }
      }

    WRITE(ok ? "Yes" : "No");
  }
}