Submit Info #487

Problem Lang User Status Time Memory
Bernoulli Number cpp beet AC 442 ms 94.09 MiB

Name Status Time Memory
0_00 AC 5 ms 0.72 MiB
100000_00 AC 101 ms 23.79 MiB
10000_00 AC 15 ms 3.47 MiB
1000_00 AC 2 ms 0.91 MiB
100_00 AC 2 ms 0.67 MiB
1_00 AC 0 ms 0.68 MiB
200000_00 AC 204 ms 47.57 MiB
300000_00 AC 402 ms 91.72 MiB
400000_00 AC 417 ms 92.84 MiB
500000_00 AC 442 ms 94.09 MiB
example_00 AC 2 ms 0.72 MiB

#include<bits/stdc++.h> using namespace std; template<typename T,T MOD = 1000000007> struct Mint{ static constexpr T mod = MOD; T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;}; Mint operator-(Mint a) const{return Mint(v)-=a;}; Mint operator*(Mint a) const{return Mint(v)*=a;}; Mint operator/(Mint a) const{return Mint(v)/=a;}; Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} bool operator <(const Mint a)const{return v <a.v;} // find x s.t. a^x = b static T log(T a,T b){ const T sq=40000; unordered_map<T, T> dp; dp.reserve(sq); Mint res(1); for(int r=0;r<sq;r++){ if(!dp.count(res.v)) dp[res.v]=r; res*=a; } Mint p=Mint(a).inv().pow(sq); res=b; for(int q=0;q<=MOD/sq+1;q++){ if(dp.count(res.v)){ T idx=q*sq+dp[res.v]; if(idx>0) return idx; } res*=p; } assert(0); return T(-1); } static Mint comb(long long n,int k){ Mint num(1),dom(1); for(int i=0;i<k;i++){ num*=Mint(n-i); dom*=Mint(i+1); } return num/dom; } }; template<typename T,T MOD> constexpr T Mint<T, MOD>::mod; template<typename T,T MOD> ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;} constexpr int bmds(int x){ const int v[] = {1012924417, 924844033, 998244353, 897581057, 645922817}; return v[x]; } constexpr int brts(int x){ const int v[] = {5, 5, 3, 3, 3}; return v[x]; } template<int X> struct NTT{ static constexpr int md = bmds(X); static constexpr int rt = brts(X); using M = Mint<int, md>; vector< vector<M> > rts,rrts; void ensure_base(int n){ if((int)rts.size()>=n) return; rts.resize(n);rrts.resize(n); for(int i=1;i<n;i<<=1){ if(!rts[i].empty()) continue; M w=M(rt).pow((md-1)/(i<<1)); M rw=w.inv(); rts[i].resize(i);rrts[i].resize(i); rts[i][0]=M(1);rrts[i][0]=M(1); for(int k=1;k<i;k++){ rts[i][k]=rts[i][k-1]*w; rrts[i][k]=rrts[i][k-1]*rw; } } } void ntt(vector<M> &as,bool f,int n=-1){ if(n==-1) n=as.size(); assert((n&(n-1))==0); ensure_base(n); for(int i=0,j=1;j+1<n;j++){ for(int k=n>>1;k>(i^=k);k>>=1); if(i>j) swap(as[i],as[j]); } for(int i=1;i<n;i<<=1){ for(int j=0;j<n;j+=i*2){ for(int k=0;k<i;k++){ M z=as[i+j+k]*(f?rrts[i][k]:rts[i][k]); as[i+j+k]=as[j+k]-z; as[j+k]+=z; } } } if(f){ M tmp=M(n).inv(); for(int i=0;i<n;i++) as[i]*=tmp; } } vector<M> multiply(vector<M> as,vector<M> bs){ int need=as.size()+bs.size()-1; int sz=1; while(sz<need) sz<<=1; as.resize(sz,M(0)); bs.resize(sz,M(0)); ntt(as,0);ntt(bs,0); for(int i=0;i<sz;i++) as[i]*=bs[i]; ntt(as,1); as.resize(need); return as; } vector<int> multiply(vector<int> as,vector<int> bs){ vector<M> am(as.size()),bm(bs.size()); for(int i=0;i<(int)am.size();i++) am[i]=M(as[i]); for(int i=0;i<(int)bm.size();i++) bm[i]=M(bs[i]); vector<M> cm=multiply(am,bm); vector<int> cs(cm.size()); for(int i=0;i<(int)cs.size();i++) cs[i]=cm[i].v; return cs; } }; template<int X> constexpr int NTT<X>::md; template<int X> constexpr int NTT<X>::rt; template<typename T> struct FormalPowerSeries{ using Poly = vector<T>; using Conv = function<Poly(Poly, Poly)>; Conv conv; FormalPowerSeries(Conv conv):conv(conv){} Poly pre(const Poly &as,int deg){ return Poly(as.begin(),as.begin()+min((int)as.size(),deg)); } Poly add(Poly as,Poly bs){ int sz=max(as.size(),bs.size()); Poly cs(sz,T(0)); for(int i=0;i<(int)as.size();i++) cs[i]+=as[i]; for(int i=0;i<(int)bs.size();i++) cs[i]+=bs[i]; return cs; } Poly sub(Poly as,Poly bs){ int sz=max(as.size(),bs.size()); Poly cs(sz,T(0)); for(int i=0;i<(int)as.size();i++) cs[i]+=as[i]; for(int i=0;i<(int)bs.size();i++) cs[i]-=bs[i]; return cs; } Poly mul(Poly as,Poly bs){ return conv(as,bs); } Poly mul(Poly as,T k){ for(auto &a:as) a*=k; return as; } // F(0) must not be 0 Poly inv(Poly as,int deg){ assert(as[0]!=T(0)); Poly rs({T(1)/as[0]}); for(int i=1;i<deg;i<<=1) rs=pre(sub(add(rs,rs),mul(mul(rs,rs),pre(as,i<<1))),i<<1); return rs; } // not zero Poly div(Poly as,Poly bs){ while(as.back()==T(0)) as.pop_back(); while(bs.back()==T(0)) bs.pop_back(); if(bs.size()>as.size()) return Poly(); reverse(as.begin(),as.end()); reverse(bs.begin(),bs.end()); int need=as.size()-bs.size()+1; Poly ds=pre(mul(as,inv(bs,need)),need); reverse(ds.begin(),ds.end()); return ds; } // F(0) must be 1 Poly sqrt(Poly as,int deg){ assert(as[0]==T(1)); T inv2=T(1)/T(2); Poly ss({T(1)}); for(int i=1;i<deg;i<<=1){ ss=pre(add(ss,mul(pre(as,i<<1),inv(ss,i<<1))),i<<1); for(T &x:ss) x*=inv2; } return ss; } Poly diff(Poly as){ int n=as.size(); Poly rs(n-1); for(int i=1;i<n;i++) rs[i-1]=as[i]*T(i); return rs; } Poly integral(Poly as){ int n=as.size(); Poly rs(n+1); rs[0]=T(0); for(int i=0;i<n;i++) rs[i+1]=as[i]/T(i+1); return rs; } // F(0) must be 1 Poly log(Poly as,int deg){ return pre(integral(mul(diff(as),inv(as,deg))),deg); } // F(0) must be 0 Poly exp(Poly as,int deg){ Poly f({T(1)}); as[0]+=T(1); for(int i=1;i<deg;i<<=1) f=pre(mul(f,sub(pre(as,i<<1),log(f,i<<1))),i<<1); return f; } Poly partition(int n){ Poly rs(n+1); rs[0]=T(1); for(int k=1;k<=n;k++){ if(1LL*k*(3*k+1)/2<=n) rs[k*(3*k+1)/2]+=T(k%2?-1LL:1LL); if(1LL*k*(3*k-1)/2<=n) rs[k*(3*k-1)/2]+=T(k%2?-1LL:1LL); } return inv(rs,n+1); } Poly bernoulli(int n){ Poly rs(n+1,1); for(int i=1;i<=n;i++) rs[i]=rs[i-1]/T(i+1); rs=inv(rs,n+1); T tmp(1); for(int i=1;i<=n;i++){ tmp*=T(i); rs[i]*=tmp; } return rs; } }; //INSERT ABOVE HERE signed main(){ cin.tie(0); ios::sync_with_stdio(0); int n; cin>>n; NTT<2> ntt; using M = NTT<2>::M; auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);}; FormalPowerSeries<M> FPS(conv); auto ps=FPS.bernoulli(n); for(int i=0;i<=n;i++){ if(i) cout<<" "; cout<<ps[i]; } cout<<endl; return 0; }