結果
問題 | No.1080 Strange Squared Score Sum |
ユーザー |
![]() |
提出日時 | 2020-06-13 00:11:14 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,367 ms / 5,000 ms |
コード長 | 19,895 bytes |
コンパイル時間 | 3,615 ms |
コンパイル使用メモリ | 240,312 KB |
最終ジャッジ日時 | 2025-01-11 03:18:07 |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 20 |
ソースコード
#include <bits/stdc++.h>using namespace std;using ll=long long;#define int ll#define rng(i,a,b) for(int i=int(a);i<int(b);i++)#define rep(i,b) rng(i,0,b)#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)#define per(i,b) gnr(i,0,b)#define pb push_back#define eb emplace_back#define a first#define b second#define bg begin()#define ed end()#define all(x) x.bg,x.ed#define si(x) int(x.size())#ifdef LOCAL#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl#else#define dmp(x) void(0)#endiftemplate<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}template<class t> using vc=vector<t>;template<class t> using vvc=vc<vc<t>>;using pi=pair<int,int>;using vi=vc<int>;template<class t,class u>ostream& operator<<(ostream& os,const pair<t,u>& p){return os<<"{"<<p.a<<","<<p.b<<"}";}template<class t> ostream& operator<<(ostream& os,const vc<t>& v){os<<"{";for(auto e:v)os<<e<<",";return os<<"}";}#define mp make_pair#define mt make_tuple#define one(x) memset(x,-1,sizeof(x))#define zero(x) memset(x,0,sizeof(x))#ifdef LOCALvoid dmpr(ostream&os){os<<endl;}template<class T,class... Args>void dmpr(ostream&os,const T&t,const Args&... args){os<<t<<" ";dmpr(os,args...);}#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)#else#define dmp2(...) void(0)#endifusing uint=unsigned;using ull=unsigned long long;template<class t,size_t n>ostream& operator<<(ostream&os,const array<t,n>&a){return os<<vc<t>(all(a));}template<int i,class T>void print_tuple(ostream&,const T&){}template<int i,class T,class H,class ...Args>void print_tuple(ostream&os,const T&t){if(i)os<<",";os<<get<i>(t);print_tuple<i+1,T,Args...>(os,t);}template<class ...Args>ostream& operator<<(ostream&os,const tuple<Args...>&t){os<<"{";print_tuple<0,tuple<Args...>,Args...>(os,t);return os<<"}";}template<class t>void print(t x,int suc=1){cout<<x;if(suc==1)cout<<"\n";if(suc==2)cout<<" ";}ll read(){ll i;cin>>i;return i;}vi readvi(int n,int off=0){vi v(n);rep(i,n)v[i]=read()+off;return v;}template<class T>void print(const vector<T>&v,int suc=1){rep(i,v.size())print(v[i],i==int(v.size())-1?suc:2);}string readString(){string s;cin>>s;return s;}template<class T>T sq(const T& t){return t*t;}//#define CAPITALvoid yes(bool ex=true){#ifdef CAPITALcout<<"YES"<<"\n";#elsecout<<"Yes"<<"\n";#endifif(ex)exit(0);}void no(bool ex=true){#ifdef CAPITALcout<<"NO"<<"\n";#elsecout<<"No"<<"\n";#endifif(ex)exit(0);}void possible(bool ex=true){#ifdef CAPITALcout<<"POSSIBLE"<<"\n";#elsecout<<"Possible"<<"\n";#endifif(ex)exit(0);}void impossible(bool ex=true){#ifdef CAPITALcout<<"IMPOSSIBLE"<<"\n";#elsecout<<"Impossible"<<"\n";#endifif(ex)exit(0);}constexpr ll ten(int n){return n==0?1:ten(n-1)*10;}const ll infLL=LLONG_MAX/3;#ifdef intconst int inf=infLL;#elseconst int inf=INT_MAX/2-100;#endifint topbit(signed t){return t==0?-1:31-__builtin_clz(t);}int topbit(ll t){return t==0?-1:63-__builtin_clzll(t);}int botbit(signed a){return a==0?32:__builtin_ctz(a);}int botbit(ll a){return a==0?64:__builtin_ctzll(a);}int popcount(signed t){return __builtin_popcount(t);}int popcount(ll t){return __builtin_popcountll(t);}bool ispow2(int i){return i&&(i&-i)==i;}ll mask(int i){return (ll(1)<<i)-1;}bool inc(int a,int b,int c){return a<=b&&b<=c;}template<class t> void mkuni(vc<t>&v){sort(all(v));v.erase(unique(all(v)),v.ed);}ll rand_int(ll l, ll r) { //[l, r]#ifdef LOCALstatic mt19937_64 gen;#elsestatic mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());#endifreturn uniform_int_distribution<ll>(l, r)(gen);}template<class t>void myshuffle(vc<t>&a){rep(i,si(a))swap(a[i],a[rand_int(0,i)]);}template<class t>int lwb(const vc<t>&v,const t&a){return lower_bound(all(v),a)-v.bg;}using uint=unsigned;using ull=unsigned long long;struct modinfo{uint mod,root;};template<modinfo const&ref>struct modular{static constexpr uint const &mod=ref.mod;static modular root(){return modular(ref.root);}uint v;//modular(initializer_list<uint>ls):v(*ls.bg){}modular(ll vv=0){s(vv%mod+mod);}modular& s(uint vv){v=vv<mod?vv:vv-mod;return *this;}modular operator-()const{return modular()-*this;}modular& operator+=(const modular&rhs){return s(v+rhs.v);}modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}modular&operator*=(const modular&rhs){v=ull(v)*rhs.v%mod;return *this;}modular&operator/=(const modular&rhs){return *this*=rhs.inv();}modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}modular pow(int n)const{modular res(1),x(*this);while(n){if(n&1)res*=x;x*=x;n>>=1;}return res;}modular inv()const{return pow(mod-2);}/*modular inv()const{int x,y;int g=extgcd(v,mod,x,y);assert(g==1);if(x<0)x+=mod;return modular(x);}*/friend modular operator+(int x,const modular&y){return modular(x)+y;}friend modular operator-(int x,const modular&y){return modular(x)-y;}friend modular operator*(int x,const modular&y){return modular(x)*y;}friend modular operator/(int x,const modular&y){return modular(x)/y;}friend ostream& operator<<(ostream&os,const modular&m){return os<<m.v;}friend istream& operator>>(istream&is,modular&m){ll x;is>>x;m=modular(x);return is;}bool operator<(const modular&r)const{return v<r.v;}bool operator==(const modular&r)const{return v==r.v;}bool operator!=(const modular&r)const{return v!=r.v;}explicit operator bool()const{return v;}};//#define USE_GOOD_MOD//size of input must be a power of 2//output of forward fmt is bit-reversed//output elements are in the range [0,mod*4)//input of inverse fmt should be bit-reversedtemplate<class mint>void inplace_fmt(const int n,mint*const f,bool inv){static constexpr uint mod=mint::mod;static constexpr uint mod2=mod*2;static const int L=30;static mint g[L],ig[L],p2[L];if(g[0].v==0){rep(i,L){mint w=-mint::root().pow(((mod-1)>>(i+2))*3);g[i]=w;ig[i]=w.inv();p2[i]=mint(1<<i).inv();}}if(!inv){int b=n;if(b>>=1){//input:[0,mod)rep(i,b){uint x=f[i+b].v;f[i+b].v=f[i].v+mod-x;f[i].v+=x;}}if(b>>=1){//input:[0,mod*2)mint p=1;for(int i=0,k=0;i<n;i+=b*2){rng(j,i,i+b){uint x=(f[j+b]*p).v;f[j+b].v=f[j].v+mod-x;f[j].v+=x;}p*=g[__builtin_ctz(++k)];}}while(b){if(b>>=1){//input:[0,mod*3)mint p=1;for(int i=0,k=0;i<n;i+=b*2){rng(j,i,i+b){uint x=(f[j+b]*p).v;f[j+b].v=f[j].v+mod-x;f[j].v+=x;}p*=g[__builtin_ctz(++k)];}}if(b>>=1){//input:[0,mod*4)mint p=1;for(int i=0,k=0;i<n;i+=b*2){rng(j,i,i+b){uint x=(f[j+b]*p).v;f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);f[j+b].v=f[j].v+mod-x;f[j].v+=x;}p*=g[__builtin_ctz(++k)];}}}}else{int b=1;if(b<n/2){//input:[0,mod)mint p=1;for(int i=0,k=0;i<n;i+=b*2){rng(j,i,i+b){ull x=f[j].v+mod-f[j+b].v;f[j].v+=f[j+b].v;f[j+b].v=x*p.v%mod;}p*=ig[__builtin_ctz(++k)];}b<<=1;}for(;b<n/2;b<<=1){mint p=1;for(int i=0,k=0;i<n;i+=b*2){rng(j,i,i+b/2){//input:[0,mod*2)ull x=f[j].v+mod2-f[j+b].v;f[j].v+=f[j+b].v;f[j].v=(f[j].v)<mod2?f[j].v:f[j].v-mod2;f[j+b].v=x*p.v%mod;}rng(j,i+b/2,i+b){//input:[0,mod)ull x=f[j].v+mod-f[j+b].v;f[j].v+=f[j+b].v;f[j+b].v=x*p.v%mod;}p*=ig[__builtin_ctz(++k)];}}if(b<n){//input:[0,mod*2)rep(i,b){uint x=f[i+b].v;f[i+b].v=f[i].v+mod2-x;f[i].v+=x;}}mint z=p2[__lg(n)];rep(i,n)f[i]*=z;}}template<class mint>void inplace_fmt(vector<mint>&f,bool inv){inplace_fmt(si(f),f.data(),inv);}template<class mint>void half_fmt(const int n,mint*const f){static constexpr uint mod=mint::mod;static constexpr uint mod2=mod*2;static const int L=30;static mint g[L],h[L];if(g[0].v==0){rep(i,L){g[i]=-mint::root().pow(((mod-1)>>(i+2))*3);h[i]=mint::root().pow((mod-1)>>(i+2));}}int b=n;int lv=0;if(b>>=1){//input:[0,mod)mint p=h[lv++];for(int i=0,k=0;i<n;i+=b*2){rng(j,i,i+b){uint x=(f[j+b]*p).v;f[j+b].v=f[j].v+mod-x;f[j].v+=x;}p*=g[__builtin_ctz(++k)];}}if(b>>=1){//input:[0,mod*2)mint p=h[lv++];for(int i=0,k=0;i<n;i+=b*2){rng(j,i,i+b){uint x=(f[j+b]*p).v;f[j+b].v=f[j].v+mod-x;f[j].v+=x;}p*=g[__builtin_ctz(++k)];}}while(b){if(b>>=1){//input:[0,mod*3)mint p=h[lv++];for(int i=0,k=0;i<n;i+=b*2){rng(j,i,i+b){uint x=(f[j+b]*p).v;f[j+b].v=f[j].v+mod-x;f[j].v+=x;}p*=g[__builtin_ctz(++k)];}}if(b>>=1){//input:[0,mod*4)mint p=h[lv++];for(int i=0,k=0;i<n;i+=b*2){rng(j,i,i+b){uint x=(f[j+b]*p).v;f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);f[j+b].v=f[j].v+mod-x;f[j].v+=x;}p*=g[__builtin_ctz(++k)];}}}}template<class mint>void half_fmt(vector<mint>&f){half_fmt(si(f),f.data());}#ifdef USE_GOOD_MODtemplate<class mint>vc<mint> multiply(vc<mint> x,const vc<mint>&y,bool same=false){int n=si(x)+si(y)-1;int s=1;while(s<n)s*=2;x.resize(s);inplace_fmt(x,false);if(!same){vc<mint> z(s);rep(i,si(y))z[i]=y[i];inplace_fmt(z,false);rep(i,s)x[i]*=z[i];}else{rep(i,s)x[i]*=x[i];}inplace_fmt(x,true);x.resize(n);return x;}#else//59501818244292734739283969-1=5.95*10^25 までの値を正しく計算//最終的な列の大きさが 2^24 までなら動く//最終的な列の大きさが 2^20 以下のときは,下の 3 つの素数を使ったほうが速い(は?)//VERIFY: yosupo//Yukicoder No980 (same=true)namespace arbitrary_convolution{//constexpr modinfo base0{167772161,3};//2^25 * 5 + 1//constexpr modinfo base1{469762049,3};//2^26 * 7 + 1//constexpr modinfo base2{754974721,11};//2^24 * 45 + 1constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1constexpr modinfo base2{1053818881,7};//2^20 * 1005 + 1using mint0=modular<base0>;using mint1=modular<base1>;using mint2=modular<base2>;template<class t,class mint>vc<t> sub(const vc<mint>&x,const vc<mint>&y,bool same=false){int n=si(x)+si(y)-1;int s=1;while(s<n)s*=2;vc<t> z(s);rep(i,si(x))z[i]=x[i].v;inplace_fmt(z,false);if(!same){vc<t> w(s);rep(i,si(y))w[i]=y[i].v;inplace_fmt(w,false);rep(i,s)z[i]*=w[i];}else{rep(i,s)z[i]*=z[i];}inplace_fmt(z,true);z.resize(n);return z;}template<class mint>vc<mint> multiply(const vc<mint>&x,const vc<mint>&y,bool same=false){auto d0=sub<mint0>(x,y,same);auto d1=sub<mint1>(x,y,same);auto d2=sub<mint2>(x,y,same);int n=si(d0);vc<mint> res(n);static const mint1 r01=mint1(mint0::mod).inv();static const mint2 r02=mint2(mint0::mod).inv();static const mint2 r12=mint2(mint1::mod).inv();static const mint2 r02r12=r02*r12;static const mint w1=mint(mint0::mod);static const mint w2=w1*mint(mint1::mod);rep(i,n){ull a=d0[i].v;ull b=(d1[i].v+mint1::mod-a)*r01.v%mint1::mod;ull c=((d2[i].v+mint2::mod-a)*r02r12.v+(mint2::mod-b)*r12.v)%mint2::mod;res[i].v=(a+b*w1.v+c*w2.v)%mint::mod;}return res;}}using arbitrary_convolution::multiply;#endiftemplate<class mint>struct Poly:public vc<mint>{template<class...Args>Poly(Args...args):vc<mint>(args...){}Poly(initializer_list<mint>init):vc<mint>(all(init)){}int size()const{return vc<mint>::size();}void ups(int s){if(size()<s)this->resize(s,0);}Poly low(int s)const{return Poly(this->bg,this->bg+min(max(s,int(1)),size()));}Poly rev()const{auto r=*this;reverse(all(r));return r;}Poly operator>>(int x)const{assert(x<size());Poly res(size()-x);rep(i,size()-x)res[i]=(*this)[i+x];return res;}Poly operator<<(int x)const{Poly res(size()+x);rep(i,size())res[i+x]=(*this)[i];return res;}mint freq(int i)const{return i<size()?(*this)[i]:0;}Poly operator-()const{Poly res=*this;for(auto&v:res)v=-v;return res;}Poly& operator+=(const Poly&r){ups(r.size());rep(i,r.size())(*this)[i]+=r[i];return *this;}template<class T>Poly& operator+=(T t){(*this)[0]+=t;return *this;}Poly& operator-=(const Poly&r){ups(r.size());rep(i,r.size())(*this)[i]-=r[i];return *this;}template<class T>Poly& operator-=(T t){(*this)[0]-=t;return *this;}template<class T>Poly& operator*=(T t){for(auto&v:*this)v*=t;return *this;}Poly& operator*=(const Poly&r){return *this=multiply(*this,r);}Poly square()const{return multiply(*this,*this,true);}#ifndef USE_GOOD_MODPoly inv(int s)const{Poly r{mint(1)/(*this)[0]};for(int n=1;n<s;n*=2)r=r*2-(r.square()*low(2*n)).low(2*n);return r.low(s);}#else//source: Section 4 of "Removing redundancy from high-precision Newton iteration"// 5/3Poly inv(int s)const{Poly r(s);r[0]=mint(1)/(*this)[0];for(int n=1;n<s;n*=2){vc<mint> f=low(2*n);f.resize(2*n);inplace_fmt(f,false);vc<mint> g=r.low(2*n);g.resize(2*n);inplace_fmt(g,false);rep(i,2*n)f[i]*=g[i];inplace_fmt(f,true);rep(i,n)f[i]=0;inplace_fmt(f,false);rep(i,2*n)f[i]*=g[i];inplace_fmt(f,true);rng(i,n,min(2*n,s))r[i]=-f[i];}return r;}#endiftemplate<class T>Poly& operator/=(T t){return *this*=mint(1)/mint(t);}Poly quotient(const Poly&r,const Poly&rri)const{int m=r.size();assert(r[m-1].v);int n=size();int s=n-m+1;if(s<=0) return {0};return (rev().low(s)*rri.low(s)).low(s).rev();}Poly& operator/=(const Poly&r){return *this=quotient(r,r.rev().inv(max(size()-r.size(),int(0))+1));}Poly& operator%=(const Poly&r){*this-=*this/r*r;return *this=low(r.size()-1);}Poly operator+(const Poly&r)const{return Poly(*this)+=r;}template<class T>Poly operator+(T t)const{return Poly(*this)+=t;}Poly operator-(const Poly&r)const{return Poly(*this)-=r;}template<class T>Poly operator-(T t)const{return Poly(*this)-=t;}template<class T>Poly operator*(T t)const{return Poly(*this)*=t;}Poly operator*(const Poly&r)const{return Poly(*this)*=r;}template<class T>Poly operator/(T t)const{return Poly(*this)/=t;}Poly operator/(const Poly&r)const{return Poly(*this)/=r;}Poly operator%(const Poly&r)const{return Poly(*this)%=r;}Poly dif()const{Poly r(max(int(0),size()-1));rep(i,r.size())r[i]=(*this)[i+1]*(i+1);return r;}Poly inte(const mint invs[])const{Poly r(size()+1,0);rep(i,size())r[i+1]=(*this)[i]*invs[i+1];return r;}//VERIFY: yosupo//opencupXIII GP of Peterhof HPoly log(int s,const mint invs[])const{assert((*this)[0]==1);if(s==1)return {0};return (low(s).dif()*inv(s-1)).low(s-1).inte(invs);}//Petrozavodsk 2019w mintay1 G//yosupo judgePoly exp(int s,const mint invs[])const{return exp2(s,invs).a;}//2つほしいときはコメントアウトの位置ずらすpair<Poly,Poly> exp2(int s,const mint invs[])const{assert((*this)[0]==mint(0));Poly f{1},g{1};for(int n=1;;n*=2){if(n>=s)break;g=g*2-(g.square()*f).low(n);//if(n>=s)break;Poly q=low(n).dif();q=q+g*(f.dif()-f*q).low(2*n-1);f=f+(f*(low(2*n)-q.inte(invs))).low(2*n);}return make_pair(f.low(s),g.low(s));}#ifndef USE_GOOD_MOD//CF250 EPoly sqrt(int s)const{assert((*this)[0]==1);static const mint half=mint(1)/mint(2);Poly r{1};for(int n=1;n<s;n*=2)r=(r+(r.inv(n*2)*low(n*2)).low(n*2))*half;return r.low(s);}#else//11/6//VERIFY: yosupoPoly sqrt(int s)const{assert((*this)[0]==1);static const mint half=mint(1)/mint(2);vc<mint> f{1},g{1},z{1};for(int n=1;n<s;n*=2){rep(i,n)z[i]*=z[i];inplace_fmt(z,true);vc<mint> delta(2*n);rep(i,n)delta[n+i]=z[i]-freq(i)-freq(n+i);inplace_fmt(delta,false);vc<mint> gbuf(2*n);rep(i,n)gbuf[i]=g[i];inplace_fmt(gbuf,false);rep(i,2*n)delta[i]*=gbuf[i];inplace_fmt(delta,true);f.resize(2*n);rng(i,n,2*n)f[i]=-half*delta[i];if(2*n>=s)break;z=f;inplace_fmt(z,false);vc<mint> eps=gbuf;rep(i,2*n)eps[i]*=z[i];inplace_fmt(eps,true);rep(i,n)eps[i]=0;inplace_fmt(eps,false);rep(i,2*n)eps[i]*=gbuf[i];inplace_fmt(eps,true);g.resize(2*n);rng(i,n,2*n)g[i]=-eps[i];}f.resize(s);return f;}#endifpair<Poly,Poly> divide(const Poly&r,const Poly&rri)const{Poly a=quotient(r,rri);Poly b=*this-a*r;return make_pair(a,b.low(r.size()-1));}//Yukicoder No.215Poly pow_mod(int n,const Poly&r)const{Poly rri=r.rev().inv(r.size());Poly cur{1},x=*this%r;while(n){if(n%2)cur=(cur*x).divide(r,rri).b;x=(x*x).divide(r,rri).b;n/=2;}return cur;}int lowzero()const{rep(i,size())if((*this)[i]!=0)return i;return size();}//VERIFY: yosupoPoly pow(int s,int p,const mint invs[])const{assert(s>0);assert(p>0);int n=size(),z=0;for(;z<n&&(*this)[z]==0;z++);if(z*p>=s)return Poly(s,0);mint c=(*this)[z],cinv=c.inv();mint d=c.pow(p);int t=s-z*p;Poly x(t);rng(i,z,min(z+t,n))x[i-z]=(*this)[i]*cinv;x=x.log(t,invs);rep(i,t)x[i]*=p;x=x.exp(t,invs);rep(i,t)x[i]*=d;Poly y(s);rep(i,t)y[z*p+i]=x[i];return y;}mint eval(mint x)const{mint r=0,w=1;for(auto v:*this){r+=w*v;w*=x;}return r;}};//extern constexpr modinfo base{998244353,3};extern constexpr modinfo base{1000000009,0};//modinfo base{1,0};using mint=modular<base>;const int vmax=(1<<21)+10;mint fact[vmax],finv[vmax],invs[vmax];void initfact(){fact[0]=1;rng(i,1,vmax){fact[i]=fact[i-1]*i;}finv[vmax-1]=fact[vmax-1].inv();for(int i=vmax-2;i>=0;i--){finv[i]=finv[i+1]*(i+1);}for(int i=vmax-1;i>=1;i--){invs[i]=finv[i]*fact[i-1];}}mint choose(int n,int k){return fact[n]*finv[n-k]*finv[k];}mint binom(int a,int b){return fact[a+b]*finv[a]*finv[b];}mint catalan(int n){return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);}template<class t>t pow_mod(t x,t n,t m){t r=1;while(n){if(n&1)r=(r*x)%m;x=(x*x)%m;n>>=1;}return r;}//assume p is a prime//yukicoder No.1025bool is_primitiveroot(int r,int p){if(!r)return false;int x=p-1;for(int i=2;i*i<=x;i++){if(x%i==0){int w=pow_mod<int>(r,(p-1)/i,p);if(w==1)return false;while(x%i==0)x/=i;}}if(x>1&&pow_mod<int>(r,(p-1)/x,p)==1)return false;return true;}//assume p is a prime//yukicoder No.1025int get_primitiveroot(int p){rng(w,1,p)if(is_primitiveroot(w,p))return w;assert(false);}vc<mint> dft(const vc<mint>&a,const mint w){int n=si(a);vc<mint> b(n);mint z=1;rep(i,n){mint cur=1;rep(j,n){b[i]+=a[j]*cur;cur*=z;}z*=w;}return b;}signed main(){cin.tie(0);ios::sync_with_stdio(0);cout<<fixed<<setprecision(20);initfact();const mint w=mint(get_primitiveroot(mint::mod)).pow((mint::mod-1)/4);int n;cin>>n;vc<vc<mint>> ans(4);rep(i,4){mint cur=w.pow(i);Poly<mint> a(n+1);rng(j,1,n+1)a[j]=cur*sq(j+1);auto b=a.exp(n+1,invs);for(auto&v:b)v*=fact[n];ans[i]=b;}const mint wi=w.inv();rng(i,1,n+1){vc<mint> a(4);rep(j,4)a[j]=ans[j][i];auto b=dft(a,wi);print((b[0]+b[1]-b[2]-b[3])/4);}}