#include using namespace std; using std::cout; using std::cin; using std::endl; using ll=long long; using ld=long double; ll ILL=2167167167167167167; const int INF=2100000000; const ll mod=998244353; #define rep(i,a) for (ll i=0;i using _pq = priority_queue, greater>; template ll LB(vector &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} template ll UB(vector &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();} template bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;} template bool chmax(T &a,const T &b){if(a void So(vector &v) {sort(v.begin(),v.end());} template void Sore(vector &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});} void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";} template void vec_out(vector &p){for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout< using namespace atcoder; //参考 https://nyaannyaan.github.io/library/fps/formal-power-series.hpp.html namespace po167{ long long rev(long long a,long long MOD){ long long D=1,C=MOD-2; while(C){ if(C&1) D=(D*a)%MOD; C>>=1; a=(a*a)%MOD; } return D; } template std::vector add_Polynomial(std::vector &p,std::vector &q){ std::vector r(std::max(p.size(),q.size())); for(int i=0;i<(int)r.size();i++){ if((int)p.size()>i) r[i]=p[i]; if((int)q.size()>i) r[i]=(r[i]+q[i])%mod; } return r; } template std::vector sub_Polynomial(std::vector &p,std::vector &q){ std::vector r(std::max(p.size(),q.size())); for(int i=0;i<(int)r.size();i++){ if((int)p.size()>i) r[i]=p[i]; if((int)q.size()>i) r[i]=(r[i]-q[i]); if(r[i]<0) r[i]=(r[i]%mod+mod)%mod; } return r; } template long long substitution_Polynomial(std::vector &p,long long x){ long long ans=0; long long D=1; for(int i=0;i std::vector differential_Polynomial(std::vector p){ int N=p.size(); std::vector r(N); for(int i=1;i std::vector Integral_Polynomial(std::vector p){ int N=p.size(); std::vector r(1+N); std::vector rev(N+1,1); for(int i=0;i1){ rev[i+1]=(mod-((mod/(i+1))*rev[mod%(i+1)])%mod)%mod; } r[i+1]=(rev[i+1]*p[i])%mod; } return r; } template std::vector slice_vec(std::vector &p,int S){ if(S>=(int)(p.size())) return p; std::vector r(S); for(int i=0;i std::vector inv_FPS(int N,int L,std::vector &p){ assert((int)p.size()==N); assert(0 q={1},tmp,tmp2; long long D=p[0]; long long C=mod-2; while(C){ if(C&1){ q[0]=(q[0]*D)%mod; } C>>=1; D=(D*D)%mod; } int S=1; while(S(tmp,convolution(q,q)); for(int i=0;i ans(S); for(int i=0;i std::vector log_FPS(int N,int L,std::vector &p){ assert(p[0]==1); auto tmp=convolution(differential_Polynomial(p),inv_FPS(N,L,p)); auto tmp3=Integral_Polynomial(tmp); return slice_vec(tmp3,L); } // return e^{f(x)} template std::vector exp_FPS(int N,int L,std::vector &p){ assert((int)p.size()==N); assert(0 q={1},tmp,tmp2,tmp3; int S=1; while(S(S/2,S,q); tmp3=sub_Polynomial(tmp,tmp2); tmp3[0]++; tmp=convolution(q,tmp3); for(int i=0;i ans(S); for(int i=0;i zero_cut(std::vector &p){ int ind=0; for(int i=0;i<(int)(p.size());i++){ if(p[i]!=0) ind=i; } return slice_vec(p,ind+1); } //return {a,b} (p=aq+b) //https://judge.yosupo.jp/submission/79020 template std::pair,std::vector> div_FPS(std::vector &p,std::vector &q){ int N=p.size(),M=q.size(); if(N(f,inv_FPS(M,N-M+1,g)); auto ans1=slice_vec(tmp,N-M+1); std::reverse(ans1.begin(),ans1.end()); tmp=convolution(ans1,q); std::vector ans2(M-1); for(int i=0;i std::vector Multipoint_Evaluation(std::vector f,std::vectorp){ int M=p.size(); if(M==0){ return {}; } std::vector size={M}; int ind=0; while(size[ind]!=1){ size.push_back((size[ind]+1)/2); ind++; } ind++; std::vector>> divisor(ind),remain(ind); for(int i=0;i(divisor[i-1][j*2],divisor[i-1][j*2+1]); }else{ divisor[i][j]=divisor[i-1][size[i-1]-1]; } } } } for(int i=ind-1;i>=0;i--){ remain[i].resize(size[i]); if(i==ind-1){ remain[i][0]=div_FPS(f,divisor[ind-1][0]).second; }else{ for(int j=0;j ans(M); for(int i=0;i std::vector multiplication_FPS(std::vector> &p){ std::queue> pq; int N=p.size(); for(int i=0;i(l,r)); } return pq.front(); } struct frac_fps{ std::vector ch; std::vector mo; }; template frac_fps add_frac_fps(frac_fps &l,frac_fps &r){ auto tmp1=convolution(l.ch,r.mo); auto tmp2=convolution(l.mo,r.ch); return {add_Polynomial(tmp1,tmp2),convolution(l.mo,r.mo)}; } template std::vector Polynomial_Interpolation(std::vector &x,std::vector &y){ int N=x.size(); assert(x.size()==y.size()); std::vector> p(N); for(int i=0;i(p); auto div=differential_Polynomial(tmp1); auto val=Multipoint_Evaluation(div,x); std::queue q; for(int i=0;i(l,r)); } long long D=1; auto ans=q.front().ch; for(int i=0;i>t; rep(i,t) solve(); } void solve(){ int N,K; cin>>N>>K; vector E(N+1),F(N+1); rep(i,N) cin>>E[i+1],F[i+1]=(mod-E[i+1])%mod; F[0]=1; auto ans0=po167::inv_FPS(1+N,N+167,F); ans0[0]=0; vector X,Y; auto _E=po167::differential_Polynomial(E); rep(i,N){ if(_E[i]!=0){ X.resize(N+1-i); Y.resize(N-i); rep(j,N-i){ Y[j]=_E[j+i]; X[j+1]=E[j+i+1]; } break; } } auto Y_inv=po167::inv_FPS((int)(Y).size(),N+3,Y); while(K>0){ ans0=po167::differential_Polynomial(ans0); ans0=convolution(ans0,X); ans0.resize(N+167); ans0=convolution(ans0,Y_inv); ans0.resize(N+167); K--; cout<<"\n"; } X.erase(X.begin()); auto X_inv=po167::inv_FPS(X.size(),N+167,X); while(K<0){ ans0.erase(ans0.begin()); ans0=convolution(ans0,X_inv); ans0.resize(N+167); ans0=convolution(ans0,Y); ans0.resize(N+167); ans0=po167::Integral_Polynomial(ans0); K++; } rep(i,N){ if(i!=0) cout<<" "; cout<