#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; struct Vec { using etype = int; // type of elements using ptype = long long; // type of product results etype x = 0, y = 0; constexpr Vec operator-() const { return {-x, -y}; } friend constexpr Vec operator+(const Vec& a, const Vec& b) { return {a.x + b.x, a.y + b.y}; } friend constexpr Vec operator-(const Vec& a, const Vec& b) { return {a.x - b.x, a.y - b.y}; } friend constexpr ptype operator*(const Vec& a, const Vec& b) { return (ptype)a.x * b.y - (ptype)a.y * b.x; } template >* = nullptr> friend constexpr Vec operator*(T c, const Vec& a) { return {c * a.x, c * a.y}; } template >* = nullptr> friend constexpr Vec operator*(const Vec& a, T c) { return c * a; } template >* = nullptr> friend constexpr Vec operator/(const Vec& a, T c) { return {a.x / c, a.y / c}; } Vec& operator+=(const Vec& a) { x += a.x; y += a.y; return *this; } Vec& operator-=(const Vec& a) { x -= a.x; y -= a.y; return *this; } template >* = nullptr> Vec& operator*=(T c) { x *= c; y *= c; return *this; } friend constexpr bool operator==(const Vec& a, const Vec& b) { return a.x == b.x && a.y == b.y; } friend constexpr bool operator!=(const Vec& a, const Vec& b) { return !(a == b); } constexpr int quadrant() const { return y > 0 ? (x > 0 ? 0 : 1) : y < 0 ? (x < 0 ? 2 : 3) : (x > 0 ? 0 : x < 0 ? 2 : -1); } friend constexpr bool operator<(const Vec& a, const Vec& b) { int qa = a.quadrant(), qb = b.quadrant(); if (qa != qb) return qa < qb; ptype p1 = (ptype)a.x * b.y, p2 = (ptype)a.y * b.x; return p1 > p2 || (p1 == p2 && (a.x != 0 ? abs(a.x) < abs(b.x) : abs(a.y) < abs(b.y))); } friend constexpr bool operator>(const Vec& a, const Vec& b) { return b < a; } friend constexpr bool operator<=(const Vec& a, const Vec& b) { return !(b < a); } friend constexpr bool operator>=(const Vec& a, const Vec& b) { return !(a < b); } constexpr int ccw(const Vec& u, const Vec& v) const { ptype p = (u - *this) * (v - *this); return p > 0 ? 1 : p < 0 ? -1 : 0; } static constexpr bool intersects(const Vec& a, const Vec& b, const Vec& c, const Vec& d) { return a.ccw(b, c) * a.ccw(b, d) <= 0 && c.ccw(d, a) * c.ccw(d, b) <= 0; } constexpr bool parallel_to(const Vec& a) const { return (ptype)x * a.y == (ptype)y * a.x; } constexpr ptype dot(const Vec& a) const { return (ptype)x * a.x + (ptype)y * a.y; } constexpr ptype norm2() const { return (ptype)x * x + (ptype)y * y; } constexpr bool is_zero() const { return x == 0 && y == 0; } constexpr Vec normalize() const { if (y == 0) return Vec{x == 0 ? 0 : 1, 0}; if (y > 0) return *this; return {-x, -y}; // etype g = gcd(x, y); // return *this / (y > 0 ? g : -g); } constexpr Vec rot90() const { return {-y, x}; } // exclusive constexpr bool in_between(const Vec& a, const Vec& b) const { Vec x = a - *this, y = b - *this; return x.parallel_to(y) && x.dot(y) < 0; } friend std::ostream& operator<< (std::ostream& os, const Vec& t) { return os << t.x << ' ' << t.y; } friend std::istream& operator>> (std::istream& os, Vec& t) { return os >> t.x >> t.y; } }; vector convex_hull(const vector& ps) { const int n = ps.size(); if (n <= 1) { if (n == 0) return {}; else return {0}; } vector ord(n); iota(ord.begin(), ord.end(), 0); sort(ord.begin(), ord.end(), [&](int i, int j) { return ps[i].y < ps[j].y || (ps[i].y == ps[j].y && ps[i].x < ps[j].x); }); vector st1, st2; for(int i: ord) { int sz = st1.size(); while(sz >= 2 && (ps[st1[sz - 1]] - ps[st1[sz - 2]]) * (ps[i] - ps[st1[sz - 1]]) <= 0) { st1.pop_back(); sz--; } st1.push_back(i); } for(int i: ord) { int sz = st2.size(); while(sz >= 2 && (ps[st2[sz - 1]] - ps[st2[sz - 2]]) * (ps[i] - ps[st2[sz - 1]]) >= 0) { st2.pop_back(); sz--; } st2.push_back(i); } assert(st1.front() == st2.front() && st1.back() == st2.back()); st1.insert(st1.end(), st2.rbegin() + 1, st2.rend() - 1); return st1; } bool solve() { int n, k; cin >> n >> k; vector p1, p2, p(n); VI c(n); rep(i, n) { cin >> p[i] >> c[i]; (c[i] == 1 ? p1 : p2).emplace_back(p[i]); } if (p1.empty() || p2.empty()) return false; { vector> d; d.reserve(n * (n - 1)); rep(i, n) rep(j, i) { Vec v = (p[i] - p[j]).normalize(); d.emplace_back(v, i); d.emplace_back(v, j); } assert(int(d.size()) == n * (n - 1)); sort(all(d)); int sz = n * (n - 1); VI idx; for(int l = 0; l < sz;) { Vec v = d[l].first; int r = l + 1; while(r < sz && d[r].first.parallel_to(v)) r++; idx.clear(); for(int i = l; i < r; i++) idx.emplace_back(d[i].second); Vec h = v.rot90(); sort(all(idx), [&](int i, int j) { return h.dot(p[j] - p[i]) > 0; }); int idxsz = idx.size(); for(int li = 0; li < idxsz; li++) { int ri = li + 1; while(ri < idxsz && h.dot(p[idx[ri]] - p[idx[li]]) == 0) ri++; sort(idx.begin() + li, idx.begin() + ri, [&](int i, int j) { return v.dot(p[j] - p[i]) > 0; }); int cnt = 0; int last = -1; for(int i = li; i < ri; i++) if (c[idx[i]] != last) { cnt++; last = c[idx[i]]; } if (cnt >= 3) return true; li = ri; } l = r; } } if (k >= 4) { VI ch1 = convex_hull(p1), ch2 = convex_hull(p2); rep(_, 2) { if (int sz = ch1.size(); sz >= 2) { ch1.emplace_back(ch1[0]); for(Vec v: p2) { int cnt = 0; rep(i, sz) cnt += Vec::intersects(v, Vec{v.x + 1, 1001001001}, p1[ch1[i]], p1[ch1[i + 1]]); if (cnt % 2 == 1) return true; } } swap(p1, p2); swap(ch1, ch2); } int sz1 = ch1.size(), sz2 = ch2.size(); if (sz1 >= 2 && sz2 >= 2) { sz1--, sz2--; rep(i, sz1) rep(j, sz2) { if (Vec::intersects(p1[ch1[i]], p1[ch1[i + 1]], p2[ch2[j]], p2[ch2[j + 1]])) { return true; } } } } return false; } } int main() { ios::sync_with_stdio(false); cin.tie(0); cout << (solve() ? "Yes\n" : "No\n"); }