#line 1 "library/Template/template.hpp" #include using namespace std; #define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++) #define ALL(v) (v).begin(),(v).end() using ll=long long int; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; templateinline bool chmax(T& a,T b){if(ainline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} #line 2 "library/Utility/fastio.hpp" #include class FastIO{ static constexpr int L=1<<16; char rdbuf[L]; int rdLeft=0,rdRight=0; inline void reload(){ int len=rdRight-rdLeft; memmove(rdbuf,rdbuf+rdLeft,len); rdLeft=0,rdRight=len; rdRight+=fread(rdbuf+len,1,L-len,stdin); } inline bool skip(){ for(;;){ while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++; if(rdLeft==rdRight){ reload(); if(rdLeft==rdRight)return false; } else break; } return true; } template::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdLeft::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft='0' and rdbuf[rdLeft]<='9' and rdLeft=rdRight)reload(); x=rdbuf[rdLeft++]; return true; } inline bool _read(string& x){ if(!skip())return false; for(;;){ int pos=rdLeft; while(pos' ')pos++; x.append(rdbuf+rdLeft,pos-rdLeft); if(rdLeft==pos)break; rdLeft=pos; if(rdLeft==rdRight)reload(); else break; } return true; } templateinline bool _read(vector& v){ for(auto& x:v){ if(!_read(x))return false; } return true; } char wtbuf[L],tmp[50]; int wtRight=0; inline void flush(){ fwrite(wtbuf,1,wtRight,stdout); wtRight=0; } inline void _write(const char& x){ if(wtRight>L-32)flush(); wtbuf[wtRight++]=x; } inline void _write(const string& x){ for(auto& c:x)_write(c); } template::value,int> =0>inline void _write(T x){ if(wtRight>L-32)flush(); if(x==0){ _write('0'); return; } else if(x<0){ _write('-'); if (__builtin_expect(x == std::numeric_limits::min(), 0)) { switch (sizeof(x)) { case 2: _write("32768"); return; case 4: _write("2147483648"); return; case 8: _write("9223372036854775808"); return; } } x=-x; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } templateinline void _write(const vector& v){ rep(i,0,v.size()){ if(i)_write(' '); _write(v[i]); } } public: FastIO(){} ~FastIO(){flush();} inline void read(){} template inline void read(Head& head,Tail&... tail){ assert(_read(head)); read(tail...); } templateinline void write(){if(ln)_write('\n');} template inline void write(const Head& head,const Tail&... tail){ if(space)_write(' '); _write(head); write(tail...); } }; /** * @brief Fast IO */ #line 3 "sol.cpp" #line 2 "library/Math/fraction.hpp" struct Frac{ ll a,b; Frac(ll _a=0){init(_a,1);} Frac(ll _a,ll _b){init(_a,_b);} Frac& init(ll _a,ll _b){ ll g=gcd(_a,_b); a=_a/g,b=_b/g; if(b<0)a=-a,b=-b; return *this; } Frac inv()const{return Frac(b,a);} Frac operator-()const{return Frac(-a,b);} Frac& operator+=(const Frac& x){return init(a*x.b+x.a*b,b*x.b);} Frac& operator-=(const Frac& x){return init(a*x.b-x.a*b,b*x.b);} Frac& operator*=(const Frac& x){return init(a*x.a,b*x.b);} Frac& operator/=(const Frac& x){return init(a*x.b,b*x.a);} Frac operator+(const Frac& x)const{return Frac(*this)+=x;} Frac operator-(const Frac& x)const{return Frac(*this)-=x;} Frac operator*(const Frac& x)const{return Frac(*this)*=x;} Frac operator/(const Frac& x)const{return Frac(*this)/=x;} bool operator<(const Frac& x)const{return a*x.b(const Frac& x)const{return x<*this;} bool operator<=(const Frac& x)const{return !(x<*this);} bool operator>=(const Frac& x)const{return !(*this=0)return 0; return 1; } Point& operator+=(const Point& p){ X+=p.X; Y+=p.Y; return *this; } Point& operator-=(const Point& p){ X-=p.X; Y-=p.Y; return *this; } Point& operator*=(const Frac& t){ X*=t,Y*=t; return *this; } Point& operator*=(const Point& p){ Frac NX=X*p.X-Y*p.Y,NY=X*p.Y+Y*p.X; X=NX,Y=NY; return *this; } Point operator+(const Point &p) const { return Point(*this) += p; } Point operator-(const Point &p) const { return Point(*this) -= p; } Point operator*(const Frac &p) const { return Point(*this) *= p; } Point operator*(const Point &p) const { return Point(*this) *= p; } Point operator-() const { return Point(-X, -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; } }; struct Line{ Point a,b; Line(){} Line(Point _a,Point _b):a(_a),b(_b){} }; struct Segment:Line{ Segment(){} Segment(Point _a,Point _b):Line(_a,_b){} }; using Poly=vector; Frac dot(const Point &a, const Point &b) { return a.X * b.X + a.Y * b.Y; } Frac cross(const Point &a, const Point &b) { return a.X * b.Y - a.Y * b.X; } Frac norm(const Point& a){return a.X*a.X+a.Y*a.Y;} bool cmp(const Point& a,const Point& b){ if(a.pos()!=b.pos())return a.pos()0)return 1; //ccw if(C<0)return -1; //cw if(dot(b,c)<0)return 2; //c,a,b if(dot(b,b)q.Y)swap(p,q); if(p.Y<0 and q.Y>0 and cross(p,q)>0)res^=1; if(cross(p,q)==0 and dot(p,q)<0)return 1; } return (res?2:0); } Poly ConvexHull(Poly& a){ int n=a.size(),k=0; if(n<=2)return a; sort(ALL(a),[](const Point& p,const Point& q){ return (p.Y==q.Y?p.X=2 and cross(res[k-1]-res[k-2],a[i]-res[k-1])<=0)k--; } for(int i=n-2,t=k+1;i>=0;res[k++]=a[i--]){ while(k>=t and cross(res[k-1]-res[k-2],a[i]-res[k-1])<=0)k--; } res.resize(k-1); return res; } Poly Cut(const Poly& a,const Line& l){ int n=a.size(); Poly res; rep(i,0,n){ Point p=a[i],q=a[(i+1)%n]; if(ccw(l.a,l.b,p)!=-1)res.push_back(p); if(ccw(l.a,l.b,p)*ccw(l.a,l.b,q)<0)res.push_back(Intersection(Line(p,q),l)); } return res; } /** * @brief Geometry(Fraction Coordinates) */ #line 5 "sol.cpp" bool solve(int N,int K,vector& x,vector& y,vector& c){ if(K==2){ sort(ALL(c)); if(c.front()==c.back())return false; else return true; } else if(K==3){ Poly R,B; rep(i,0,N){ if(c[i]==1)R.push_back(Point(x[i],y[i])); else B.push_back(Point(x[i],y[i])); } rep(_,0,2){ if(B.size()>=2){ rep(i,0,R.size()){ set done; rep(j,0,B.size()){ Point d=B[j]-R[i]; int g=gcd(d.X.a,d.Y.a); d.X/=g,d.Y/=g; if(done.count(-d)){ return true; } done.insert(d); } } } swap(R,B); } return false; } else{ Poly R,B; rep(i,0,N){ if(c[i]==1)R.push_back(Point(x[i],y[i])); else B.push_back(Point(x[i],y[i])); } R=ConvexHull(R),B=ConvexHull(B); rep(i,0,R.size())if(isContained(B,R[i])!=0){ return true; } rep(i,0,B.size())if(isContained(R,B[i])!=0){ return true; } rep(i,0,R.size())rep(j,0,B.size())if(isIntersect(Segment(R[i],R[(i+1)%R.size()]),Segment(B[j],B[(j+1)%B.size()]))){ return true; } return false; } } FastIO io; int main(){ int N,K; io.read(N,K); vector x(N),y(N),c(N); rep(i,0,N)io.read(x[i],y[i],c[i]); io.write(solve(N,K,x,y,c)?"Yes":"No"); return 0; }