#line 1 "A.cpp" // #pragma GCC target("avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; #define endl "\n" void print(){ cout << '\n'; } template void print(Head &&head, Tail &&... tail) { cout << head; if (sizeof...(Tail)) cout << ' '; print(forward(tail)...); } template void print(vector &A){ int n = A.size(); for(int i = 0; i < n; i++){ cout << A[i]; if(i == n - 1) cout << '\n'; else cout << ' '; } } template void prisep(vector &A, S sep){ int n = A.size(); for(int i = 0; i < n; i++){ cout << A[i]; if(i == n - 1) cout << '\n'; else cout << sep; } } template void print(vector> &A){ for(auto &row: A) print(row); } #line 2 "Library/C++/geometry/Point.hpp" struct Point{ long long x; long long y; Point(){} Point(long long x, long long y) : x(x), y(y) {} int area(){ if(y < 0){ if(x < 0) return 1; else return 2; } else{ if(x >= 0) return 3; else return 4; } } bool operator<(Point& rhs){ int ap = area(); int aq = rhs.area(); if(ap == aq){ if (x == 0 && y == 0) return true; return x * rhs.y > rhs.x * y; } else{ return ap < aq; } } }; #line 3 "Library/C++/geometry/cross3.hpp" long long cross3(Point &a, Point &b, Point &c){ return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x); } #line 4 "Library/C++/geometry/convexHull.hpp" vector convexHull(vector P, bool multi=true){ sort(P.begin(), P.end(), [](Point &l, Point &r){ if(l.x == r.x) return l.y < r.y; return l.x < r.x; }); vector Q; int n = P.size(); if(multi){ for(auto p:P){ while(Q.size() > 1 && cross3(Q[Q.size() - 1], Q[Q.size() - 2], p) > 0){ Q.pop_back(); } Q.push_back(p); } int t = Q.size(); for(int i = n - 2; i >= 0; i--){ Point p = P[i]; while(Q.size() > t && cross3(Q[Q.size() - 1], Q[Q.size() - 2], p) > 0){ Q.pop_back(); } Q.push_back(p); } } else{ for(auto p:P){ while(Q.size() > 1 && cross3(Q[Q.size() - 1], Q[Q.size() - 2], p) >= 0){ Q.pop_back(); } Q.push_back(p); } int t = Q.size(); for(int i = n - 2; i >= 0; i--){ Point p = P[i]; while(Q.size() > t && cross3(Q[Q.size() - 1], Q[Q.size() - 2], p) >= 0){ Q.pop_back(); } Q.push_back(p); } } Q.pop_back(); return Q; } #line 46 "A.cpp" void solve(){ int n, k; cin >> n >> k; vector R, B; int x, y, c; for(int i = 0; i < n; i++){ cin >> x >> y >> c; if(c == 1) R.push_back({x, y}); else B.push_back({x, y}); } if(R.size() == 0 || B.size() == 0){ print("No"); return; } if(R.size() > B.size()) swap(R, B); int lr = R.size(); int lb = B.size(); if(lr == 1){ for(int i = 0; i < lb; i++){ for(int j = i + 1; j < lb; j++){ auto x = cross3(B[i], B[j], R[0]); if(x == 0){ print("Yes"); return; } } } } if(k == 3){ print("No"); return; } auto BB = B; B = convexHull(B, false); lb = B.size(); for(int i = 0; i < lr; i++){ bool in_ = true; bool same = (cross3(B[lb - 1], B[0], R[i]) >= 0); for(int j = 0; j < lb - 1; j++){ bool flg = (cross3(B[j], B[j + 1], R[i]) >= 0); if(flg != same){ in_ = false; break; } } if(in_){ print("Yes"); return; } } sort(R.begin(), R.end()); int r = 0; long double pi = cos(-1); long double pi2 = 2 * pi; auto cross=[&](Point &a, Point &b, Point &c, Point &d){ bool flg1 = __int128_t(cross3(a, b, c)) * __int128_t(cross3(a, b, d)) <= 0; bool flg2 = __int128_t(cross3(c, d, a)) * __int128_t(cross3(c, d, b)) <= 0; return (flg1 && flg2); }; for(int l = 0; l < lr; l++){ while(1){ long double d = atan2(R[r].y, R[r].x) - atan2(R[l].y, R[l].x); if(d <= 0) d += pi2; if(d < pi){ r++; if(r == lr) r = 0; } else{ break; } } for(int rr = r - 100; rr <= r + 100; rr++){ int br = (rr % lr + lr) % lr; if(cross(R[l], R[br], B[0], B[lb - 1])){ print("Yes"); return; } for(int j = 0; j < lb - 1; j++){ if(cross(R[l], R[br], B[j], B[j + 1])){ print("Yes"); return; } } } } B = BB; swap(B, R); lr = R.size(); B = convexHull(B, false); lb = B.size(); for(int i = 0; i < lr; i++){ bool in_ = true; bool same = (cross3(B[lb - 1], B[0], R[i]) >= 0); for(int j = 0; j < lb - 1; j++){ bool flg = (cross3(B[j], B[j + 1], R[i]) >= 0); if(flg != same){ in_ = false; break; } } if(in_){ print("Yes"); return; } } sort(R.begin(), R.end()); r = 0; pi = cos(-1); pi2 = 2 * pi; for(int l = 0; l < lr; l++){ while(1){ long double d = atan2(R[r].y, R[r].x) - atan2(R[l].y, R[l].x); if(d <= 0) d += pi2; if(d < pi){ r++; if(r == lr) r = 0; } else{ break; } } for(int rr = r - 100; rr <= r + 100; rr++){ int br = (rr % lr + lr) % lr; if(cross(R[l], R[br], B[0], B[lb - 1])){ print("Yes"); return; } for(int j = 0; j < lb - 1; j++){ if(cross(R[l], R[br], B[j], B[j + 1])){ print("Yes"); return; } } } } print("No"); } int main(){ cin.tie(0)->sync_with_stdio(0); int t; t = 1; // cin >> t; while(t--) solve(); return 0; }