#include using namespace std; template inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template inline void chmax(T1 &a,T2 b){if(a 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 constexpr T Mint::mod; template ostream& operator<<(ostream &os,Mint m){os< class Enumeration{ using M = M_; protected: static vector fact,finv,invs; public: static void init(int n){ n=min(n,M::mod-1); int m=fact.size(); if(n=m;i--) finv[i-1]=finv[i]*M(i); for(int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1]; } static M Fact(int n){ init(n); return fact[n]; } static M Finv(int n){ init(n); return finv[n]; } static M Invs(int n){ init(n); return invs[n]; } static M C(int n,int k){ if(n vector Enumeration::fact=vector(); template vector Enumeration::finv=vector(); template vector Enumeration::invs=vector(); 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 struct NTT{ static constexpr int md = bmds(X); static constexpr int rt = brts(X); using M = Mint; vector< vector > rts,rrts; void ensure_base(int n){ if((int)rts.size()>=n) return; rts.resize(n);rrts.resize(n); for(int i=1;i &as,bool f){ int n=as.size(); assert((n&(n-1))==0); ensure_base(n); for(int i=0,j=1;j+1>1;k>(i^=k);k>>=1); if(i>j) swap(as[i],as[j]); } for(int i=1;i multiply(vector as,vector bs){ int need=as.size()+bs.size()-1; int sz=1; while(sz multiply(vector as,vector bs){ vector 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 cm=multiply(am,bm); vector cs(cm.size()); for(int i=0;i<(int)cs.size();i++) cs[i]=cm[i].v; return cs; } }; template constexpr int NTT::md; template constexpr int NTT::rt; template struct FormalPowerSeries : Enumeration { using M = M_; using super = Enumeration; using super::fact; using super::finv; using super::invs; using Poly = vector; using Conv = function; 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,M(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,M(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,M k){ for(auto &a:as) a*=k; return as; } // F(0) must not be 0 Poly inv(Poly as,int deg){ assert(as[0]!=M(0)); Poly rs({M(1)/as[0]}); for(int i=1;ias.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; } Poly mod(Poly as,Poly bs){ if(as==Poly(as.size(),0)) return Poly({0}); as=sub(as,mul(div(as,bs),bs)); if(as==Poly(as.size(),0)) return Poly({0}); while(as.back()==M(0)) as.pop_back(); return as; } // F(0) must be 1 Poly sqrt(Poly as,int deg){ assert(as[0]==M(1)); M inv2=M(1)/M(2); Poly ss({M(1)}); for(int i=1;i=deg) return Poly(deg,M(0)); as.erase(as.begin(),as.begin()+cnt); deg-=cnt*k; M c=as[0]; Poly zs(cnt*k,M(0)); Poly rs=mul(exp(mul(log(mul(as,c.inv()),deg),M(k)),deg),c.pow(k)); zs.insert(zs.end(),rs.begin(),rs.end()); return pre(zs,deg+cnt*k); } // x -> x + c Poly shift(Poly as,M c){ super::init(as.size()+1); int n=as.size(); for(int i=0;i>n>>m; vector as(n); for(int i=0;i>as[i]; NTT<2> ntt; using M = decltype(ntt)::M; using Poly = vector; using P = pair; auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);}; FormalPowerSeries FPS(conv); queue

que; for(int a:as) que.emplace(Poly({M(1)}),Poly({M(1),-M(a)})); while(que.size()>1){ auto x=que.front();que.pop(); auto y=que.front();que.pop(); Poly num=FPS.add(FPS.mul(x.first,y.second),FPS.mul(y.first,x.second)); Poly den=FPS.mul(x.second,y.second); que.emplace(num,den); } auto p=que.front(); Poly rs=FPS.mul(p.first,FPS.inv(p.second,m)); for(int i=1;i<=m;i++){ if(i!=1) cout<<' '; cout<