/** * date : 2022-12-25 15:04:27 */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N,F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(vector &v) { return next_permutation(begin(v), end(v)); } template using minpq = priority_queue, greater>; } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug #ifdef NyaanDebug #define trc(...) (void(0)) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) (void(0)) #else #define trc2(...) (void(0)) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // struct Point { using T = __int128_t; T x, y; Point() : x(0), y(0) {} Point(T x_, T y_) : x(x_), y(y_) {} Point &operator+=(const Point &p) { this->x += p.x; this->y += p.y; return *this; } Point &operator-=(const Point &p) { this->x -= p.x; this->y -= p.y; return *this; } int pos() const { if (y < 0) return -1; if (y == 0 && 0 <= x) return 0; return 1; } Point operator+(const Point &p) const { return Point(*this) += p; } Point operator-(const Point &p) const { return Point(*this) -= p; } Point operator-() const { return Point(-this->x, -this->y); } bool operator==(const Point &p) const { return x == p.x && y == p.y; } bool operator!=(const Point &p) const { return x != p.x || y != p.y; } bool operator<(const Point &p) const { return x == p.x ? y < p.y : x < p.x; } friend istream &operator>>(istream &is, Point &p) { long long x, y; is >> x >> y; p.x = x, p.y = y; return is; } friend ostream &operator<<(ostream &os, const Point &p) { os << (long long)(p.x) << " " << (long long)(p.y); return os; } }; using Points = vector; Point::T dot(const Point &a, const Point &b) { return a.x * b.x + a.y * b.y; } Point::T cross(const Point &a, const Point &b) { return a.x * b.y - a.y * b.x; } // sort by argument (-Pi ~ Pi) void ArgumentSort(Points &v) { sort(begin(v), end(v), [](Point a, Point b) { if (a.pos() != b.pos()) return a.pos() < b.pos(); return cross(a, b) > 0; }); } // 1 ... counterclockwise / 0 straight / -1 clockwise int ccw(const Point &a, const Point &b, const Point &c) { Point::T t = cross(b - a, c - a); return t < 0 ? -1 : t == 0 ? 0 : 1; } // v must have sorted by x-coordinate Points LowerHull(const Points &ps) { int N = (int)ps.size(); for (int i = 0; i < N - 1; i++) assert(ps[i].x <= ps[i + 1].x); if (N <= 2) return ps; Points convex(N); int k = 0; for (int i = 0; i < N; convex[k++] = ps[i++]) { while (k >= 2 && ccw(convex[k - 2], convex[k - 1], ps[i]) <= 0) --k; } convex.resize(k); return convex; } struct Line { Point a, b; Line() = default; Line(const Point &_a, const Point &_b) : a(_a), b(_b) {} }; bool onto(Line l, Point m) { auto A = cross(l.b - l.a, m - l.a); if (A != 0) return false; auto d1 = dot(l.b - l.a, m - l.a); auto d2 = dot(l.b - l.a, l.b - l.a); if (0 <= d1 and d1 <= d2) return true; return false; } bool cross_point(Line l, Line m) { auto A = cross(l.b - l.a, m.a - l.a); auto B = cross(l.b - l.a, m.b - l.a); if (A == 0 and onto(l, m.a)) return true; if (B == 0 and onto(l, m.b)) return true; swap(l, m); auto C = cross(l.b - l.a, m.a - l.a); auto D = cross(l.b - l.a, m.b - l.a); if (C == 0 and onto(l, m.a)) return true; if (D == 0 and onto(l, m.b)) return true; if (A == 0 or B == 0 or C == 0 or D == 0) return false; if ((A > 0) == (B > 0)) return false; if ((C > 0) == (D > 0)) return false; return true; } Points UpperHull(const Points &ps) { int N = (int)ps.size(); for (int i = 0; i < N - 1; i++) assert(ps[i].x <= ps[i + 1].x); if (N <= 2) return ps; Points convex(N); int k = 0; for (int i = 0; i < N; convex[k++] = ps[i++]) { while (k >= 2 && ccw(convex[k - 2], convex[k - 1], ps[i]) >= 0) --k; } convex.resize(k); return convex; } Points ConvexHull(const Points &ps) { int N = (int)ps.size(); for (int i = 0; i < N - 1; i++) assert(ps[i].x <= ps[i + 1].x); if (N <= 2) return ps; Points convex(2 * N); int k = 0; for (int i = 0; i < N; convex[k++] = ps[i++]) { while (k >= 2 && ccw(convex[k - 2], convex[k - 1], ps[i]) <= 0) --k; } for (int i = N - 2, t = k + 1; i >= 0; convex[k++] = ps[i--]) { while (k >= t && ccw(convex[k - 2], convex[k - 1], ps[i]) <= 0) --k; } convex.resize(k - 1); return convex; } using namespace Nyaan; void q() { inl(N, K); Points c1, c2; rep(i, N) { inl(x, y, c); (c == 1 ? c1 : c2).emplace_back(x, y); } rep(_, 2) { each(p, c2) { if (sz(c1) <= 1) continue; Points ps; each(q, c1) ps.push_back(q - p); ArgumentSort(ps); trc(ps); for (int i = 0, j = 1; i < sz(ps); i++) { while (j != i and cross(ps[i], ps[j]) > 0) { j++; if (j == sz(ps)) j = 0; } trc(ps[i], ps[j]); if (dot(ps[i], ps[j]) < 0 and cross(ps[i], ps[j]) == 0) die("Yes"); } } swap(c1, c2); } trc("line end"); sort(all(c1)); sort(all(c2)); c1 = ConvexHull(c1); c2 = ConvexHull(c2); trc(c1); trc(c2); rep(_, 2) { // p が凸包 c1 に接する/内包されるか? each(p, c2) { int ok = 1; int not_on = 0; rep(i, sz(c1)) { if (sz(c1) == 1) break; auto p1 = c1[i]; auto p2 = c1[(i + 1) % sz(c1)]; // (x2-x1,y2-y1) x (xp-x1,yp-y1) i128 cross = ::cross(p2 - p1, p - p1); if (cross == 0) { // 内部か? if (onto({p1, p2}, p)) { die("Yes"); } } else if (cross < 0) { ok = 0; } else { not_on = 1; } if (ok == 0) break; } if (ok and not_on and K >= 4) die("Yes"); } swap(c1, c2); } if (K == 3) die("No"); rep(i, sz(c1)) { Line l1{c1[i], c1[(i + 1) % sz(c1)]}; rep(j, sz(c2)) { Line l2{c2[j], c2[(j + 1) % sz(c2)]}; if (cross_point(l1, l2)) die("Yes"); } } out("No"); } void Nyaan::solve() { int t = 1; // in(t); while (t--) q(); }