Submit Info #54697

Problem Lang User Status Time Memory
Multipoint Evaluation cpp TKO919 AC 841 ms 68.30 MiB

ケース詳細
Name Status Time Memory
example_00 AC 34 ms 23.72 MiB
example_01 AC 34 ms 23.68 MiB
max_random_00 AC 841 ms 68.26 MiB
max_random_01 AC 836 ms 68.30 MiB
random_00 AC 278 ms 36.37 MiB
random_01 AC 267 ms 35.91 MiB
random_02 AC 781 ms 67.39 MiB
zero_00 AC 33 ms 23.68 MiB

#define _USE_MATH_DEFINES #include <bits/stdc++.h> using namespace std; //template #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; const double eps=1e-12; template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;} template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} template<int mod=998244353>struct fp { int v; static int get_mod(){return mod;} int inv() const{ int tmp,a=v,b=mod,x=1,y=0; while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y); if(x<0){x+=mod;} return x; } fp(ll x=0){init(x%mod+mod);} fp& init(int x){v=(x<mod?x:x-mod); return *this;} fp operator-()const{return fp()-*this;} fp pow(ll t){fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;} fp& operator+=(const fp& x){return init(v+x.v);} fp& operator-=(const fp& x){return init(v+mod-x.v);} fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;} fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;} fp operator+(const fp& x)const{return fp(*this)+=x;} fp operator-(const fp& x)const{return fp(*this)-=x;} fp operator*(const fp& x)const{return fp(*this)*=x;} fp operator/(const fp& x)const{return fp(*this)/=x;} bool operator==(const fp& x)const{return v==x.v;} bool operator!=(const fp& x)const{return v!=x.v;} }; using Fp=fp<>; template<typename T>struct factorial { vector<T> Fact,Finv,Inv; factorial(int maxx){ Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx); Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1; rep(i,2,maxx){Fact[i]=Fact[i-1]*i;} Finv[maxx-1]=Fact[maxx-1].inv(); for(int i=maxx-1;i>=2;i--){Finv[i-1]=Finv[i]*i; Inv[i]=Finv[i]*Fact[i-1];} } T fact(int n,bool inv=0){if(n<0)return 0; return (inv?Finv[n]:Fact[n]);} T inv(int n){if(n<0)return 0; return Inv[n];} T nPr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(n-r,inv^1);} T nCr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(r,inv^1)*fact(n-r,inv^1);} T nHr(int n,int r,bool inv=0){return nCr(n+r-1,r,inv);} }; template<typename T=Fp,unsigned p=3>struct NTT{ vector<T> rt,irt; NTT(int lg=21){ unsigned m=T::get_mod()-1; T prt=p; rt.resize(lg); irt.resize(lg); rep(k,0,lg){ rt[k]=-prt.pow(m>>(k+2)); irt[k]=rt[k].inv(); } } void ntt(vector<T>& f,bool inv=0){ int n=f.size(); if(inv){ for(int m=1;m<n;m<<=1){ T w=1; for(int s=0,t=0;s<n;s+=m*2){ for(int i=s,j=s+m;i<s+m;i++,j++){ auto x=f[i],y=f[j]; f[i]=x+y; f[j]=(x-y)*w; } w*=irt[__builtin_ctz(++t)]; } } T mul=T(n).inv(); rep(i,0,n)f[i]*=mul; }else{ for(int m=n;m>>=1;){ T w=1; for(int s=0,t=0;s<n;s+=m*2){ for(int i=s,j=s+m;i<s+m;i++,j++){ auto x=f[i],y=f[j]*w; f[i]=x+y; f[j]=x-y; } w*=rt[__builtin_ctz(++t)]; } } } } vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0){ if(a.empty() or b.empty())return vector<T>(); int n=a.size()+b.size()-1,m=1<<__lg(n*2-1); vector<T> res(m); rep(i,0,a.size()){res[i]=a[i];} ntt(res); if(same)rep(i,0,m)res[i]*=res[i]; else{ vector<T> c(m); rep(i,0,b.size())c[i]=b[i]; ntt(c); rep(i,0,m)res[i]*=c[i]; } ntt(res,1); res.resize(n); return res; } }; NTT<Fp,3> ntt; vector<Fp> mult(const vector<Fp>& a,const vector<Fp>& b,bool same=0){ return ntt.mult(a,b,same); } factorial<Fp> fact(2010101); template<typename T=Fp>struct Poly:vector<T>{ Poly(int n=0){this->assign(n,T());} Poly(const vector<T>& f){this->assign(ALL(f));} T eval(const T& x){T res; for(auto& v:*this)res*=x,res+=v; return res;} Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;} void shrink(){while(!this->empty() and this->back()==0)this->pop_back();} Poly inv()const{ assert(this->front()!=0); const int n=this->size(); Poly res(1); res.front()=T(1)/this->front(); for(int k=1;k<n;k<<=1){ Poly g=res,h=*this; h.resize(k*2); res.resize(k*2); g=(g.square()*h); g.resize(k*2); rep(i,k,min(k*2,n))res[i]-=g[i]; } res.resize(n); return res; } Poly square()const{return Poly(mult(*this,*this,1));} Poly operator+(const Poly& g)const{return Poly(*this)+=g;} Poly operator-(const Poly& g)const{return Poly(*this)-=g;} Poly operator*(const Poly& g)const{return Poly(*this)*=g;} Poly operator/(const Poly& g)const{return Poly(*this)/=g;} Poly operator%(const Poly& g)const{return Poly(*this)%=g;} Poly& operator+=(const Poly& g){ if(g.size()>this->size())this->resize(g.size()); rep(i,0,g.size()){(*this)[i]+=g[i];} shrink(); return *this; } Poly& operator-=(const Poly& g){ if(g.size()>this->size())this->resize(g.size()); rep(i,0,g.size()){(*this)[i]-=g[i];} shrink(); return *this; } Poly& operator*=(const Poly& g){ *this=mult(*this,g,0); shrink(); return *this; } Poly& operator/=(const Poly& g){ if(g.size()>this->size()){ this->clear(); return *this; } Poly g2=g; reverse(ALL(*this)); reverse(ALL(g2)); int n=this->size()-g2.size()+1; this->resize(n); g2.resize(n); *this*=g2.inv_fast(); this->resize(n); // reverse(ALL(*this)); shrink(); return *this; } Poly& operator%=(const Poly& g){*this-=*this/g*g; shrink(); return *this;} Poly diff()const{ Poly res(this->size()-1); rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1); return res; } Poly inte()const{ Poly res(this->size()+1); for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]*fact.inv(i); return res; } Poly log()const{ assert(this->front()==1); const int n=this->size(); Poly res=diff()*inv_fast(); res=res.inte(); // res.resize(n); return res; } Poly exp()const{ assert(this->front()==0); const int n=this->size(); Poly res(1),g(1); res.front()=g.front()=1; for(int k=1;k<n;k<<=1){ g=(g+g-g.square()*res); g.resize(k); Poly q=*this; q.resize(k); q=q.diff(); Poly w=(q+g*(res.diff()-res*q)),t=*this; w.resize(k*2-1); t.resize(k*2); res=(res+res*(t-w.inte())); res.resize(k*2); } res.resize(n); return res; } Poly shift(const int& c)const{ const int n=this->size(); Poly res=*this,g(n); g[1]=c; g=g.exp_fast(); // rep(i,0,n){res[i]*=fact.fact(i);} res=res.rev(); res*=g; res.resize(n); res=res.rev(); rep(i,0,n){res[i]*=fact.fact(i,1);} return res; } Poly inv_fast()const{ const int n=this->size(); Poly res(1); res.front()=T(1)/this->front(); for(int k=1;k<n;k<<=1){ Poly f(k*2),g(k*2); rep(i,0,min(n,k*2))f[i]=(*this)[i]; rep(i,0,k)g[i]=res[i]; ntt.ntt(f); ntt.ntt(g); rep(i,0,k*2)f[i]*=g[i]; ntt.ntt(f,1); rep(i,0,k){f[i]=0; f[i+k]=-f[i+k];} ntt.ntt(f); rep(i,0,k*2)f[i]*=g[i]; ntt.ntt(f,1); rep(i,0,k)f[i]=res[i]; swap(res,f); } res.resize(n); return res; } Poly exp_fast()const{ const int n=this->size(); if(n==1)return Poly({T(1)}); Poly b(2),c(1),z1,z2(2); b[0]=c[0]=z2[0]=z2[1]=1; b[1]=(*this)[1]; for(int k=2;k<n;k<<=1){ Poly y=b; y.resize(k*2); ntt.ntt(y); z1=z2; Poly z(k); rep(i,0,k)z[i]=y[i]*z1[i]; ntt.ntt(z,1); rep(i,0,k>>1)z[i]=0; ntt.ntt(z); rep(i,0,k)z[i]*=-z1[i]; ntt.ntt(z,1); c.insert(c.end(),z.begin()+(k>>1),z.end()); z2=c; z2.resize(k*2); ntt.ntt(z2); Poly x=*this; x.resize(k); x=x.diff(); x.resize(k); ntt.ntt(x); rep(i,0,k)x[i]*=y[i]; ntt.ntt(x,1); Poly bb=b.diff(); rep(i,0,k-1)x[i]-=bb[i]; x.resize(k*2); rep(i,0,k-1){x[k+i]=x[i]; x[i]=0;} ntt.ntt(x); rep(i,0,k*2)x[i]*=z2[i]; ntt.ntt(x,1); x.pop_back(); x=x.inte(); rep(i,k,min(n,k*2))x[i]+=(*this)[i]; rep(i,0,k)x[i]=0; ntt.ntt(x); rep(i,0,k*2)x[i]*=y[i]; ntt.ntt(x,1); b.insert(b.end(),x.begin()+k,x.end()); } b.resize(n); return b; } Poly pow(ll t){ int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++; Poly res(n); if(t*k>=n)return res; n-=t*k; Poly g(n); T c=(*this)[k],ic=T(1)/c; rep(i,0,n)g[i]=(*this)[i+k]*ic; g=g.log(); for(auto& x:g)x*=t; g=g.exp_fast(); // c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res; } }; template<typename T>struct MultiEval{ int m,n; vector<Poly<T>> t; MultiEval(vector<T>& v){ m=v.size(),n=1; while(n<m)n<<=1; t.resize(n<<1); rep(i,0,n){ T w=(i<m?v[i]:0); t[n+i]=Poly<T>({-w,T(1)}); } for(int i=n-1;i;i--)t[i]=t[i*2]*t[i*2+1]; } vector<T> run(const vector<T>& f){ vector<Poly<T>> c(n*2); auto v=t[1].rev(); v.resize(f.size()); v=v.inv().rev()*Poly<T>(f); v.erase(v.begin(),v.begin()+f.size()-1); v.resize(n); reverse(ALL(v)); c[1]=v; rep(i,1,n){ int d=c[i].size(); rep(k,0,2){ auto add=t[i*2+(k^1)]; add.resize(d/2+1); add=add.rev(); add=mult(add,c[i]); add.resize(d); c[i*2+k]=vector<T>(add.begin()+d/2,add.end()); } } vector<T> res(m); rep(i,0,m)res[i]=c[n+i][0]; return res; } vector<T> build(vector<T>& ys){ auto w=t[1].rev(); w.resize(m+1); auto vs=run(w.rev().diff()); rep(i,0,m)ys[i]/=vs[i]; vector<Poly<T>> c(n*2); rep(i,0,n){ if(i<m)c[n+i]=Poly<T>({ys[i]}); else c[n+i]=Poly<T>({T()}); } for(int i=n-1;i;i--)c[i]=c[i*2]*t[i*2+1]+c[i*2+1]*t[i*2]; c[1]=vector<T>(c[1].begin()+(n-m),c[1].end()); c[1].resize(m); return c[1]; } }; int main(){ int n,m; cin>>n>>m; vector<Fp> c(n),p(m); rep(i,0,n){ int x; cin>>x; c[i]=x; } rep(i,0,m){ int x; cin>>x; p[i]=x; } MultiEval<Fp> base(p); auto res=base.run(c); rep(i,0,m)cout<<res[i].v<<'\n'; return 0; }