結果
| 問題 | No.1080 Strange Squared Score Sum |
| ユーザー |
 maroon_kuri
|
| 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 |
（要ログイン）
| 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)
#endif
template<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 LOCAL
void 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)
#endif
using 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 CAPITAL
void yes(bool ex=true){
#ifdef CAPITAL
cout<<"YES"<<"\n";
#else
cout<<"Yes"<<"\n";
#endif
if(ex)exit(0);
}
void no(bool ex=true){
#ifdef CAPITAL
cout<<"NO"<<"\n";
#else
cout<<"No"<<"\n";
#endif
if(ex)exit(0);
}
void possible(bool ex=true){
#ifdef CAPITAL
cout<<"POSSIBLE"<<"\n";
#else
cout<<"Possible"<<"\n";
#endif
if(ex)exit(0);
}
void impossible(bool ex=true){
#ifdef CAPITAL
cout<<"IMPOSSIBLE"<<"\n";
#else
cout<<"Impossible"<<"\n";
#endif
if(ex)exit(0);
}
constexpr ll ten(int n){
return n==0?1:ten(n-1)*10;
}
const ll infLL=LLONG_MAX/3;
#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif
int 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 LOCAL
static mt19937_64 gen;
#else
static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
#endif
return 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-reversed
template<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_MOD
template<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 + 1
constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1
constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1
constexpr modinfo base2{1053818881,7};//2^20 * 1005 + 1
using 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;
#endif
template<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_MOD
Poly 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"
// 5/3
Poly 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;
}
#endif
template<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 H
Poly 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 judge
Poly 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 E
Poly 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: yosupo
Poly 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;
}
#endif
pair<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.215
Poly 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: yosupo
Poly 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.1025
bool 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.1025
int 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);
}
}