結果
| 問題 |
No.1145 Sums of Powers
|
| ユーザー |
 Taiki0715
|
| 提出日時 | 2025-07-29 15:27:11 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 247 ms / 2,000 ms |
| コード長 | 18,121 bytes |
| コンパイル時間 | 1,626 ms |
| コンパイル使用メモリ | 120,224 KB |
| 実行使用メモリ | 8,940 KB |
| 最終ジャッジ日時 | 2025-07-29 15:27:15 |
| 合計ジャッジ時間 | 3,467 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 6 |
ソースコード
#include<iostream>
#include<vector>
#include<cassert>
#include<optional>
#include<algorithm>
#include<array>
#include<type_traits>
#include<numeric>
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits<=32),T>pow_mod(T a,T n,T mod){
using u64=unsigned long long;
u64 res=1;
while(n>0){
if(n&1)res=((u64)res*a)%mod;
a=((u64)a*a)%mod;
n>>=1;
}
return T(res);
}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),T>pow_mod(T a,T n,T mod){
using u128=__uint128_t;
u128 res=1;
while(n>0){
if(n&1)res=((u128)res*a)%mod;
a=((u128)a*a)%mod;
n>>=1;
}
return T(res);
}
constexpr int primitive_root_constexpr(int x){
if(x==167772161)return 3;
if(x==469762049)return 3;
if(x==754974721)return 11;
if(x==880803841)return 26;
if(x==998244353)return 3;
if(x==2)return 1;
int x2=x;
int p[20]={};
int c=0;
x--;
for(int i=2;i*i<=x;i++){
if(x%i==0){
p[c++]=i;
while(x%i==0)x/=i;
}
}
if(x!=1)p[c++]=x;
x=x2;
for(int g=2;;g++){
bool ok=true;
for(int i=0;i<c;i++)if(pow_mod(g,(x-1)/p[i],x)==1){
ok=false;
break;
}
if(ok)return g;
}
}
#include<limits>
#include<concepts>
template<typename T>
constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>msb(T n){return n==0?-1:31-__builtin_clz(n);}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>msb(T n){return n==0?-1:63-__builtin_clzll(n);}
template<typename T>
constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>lsb(T n){return n==0?-1:__builtin_ctz(n);}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>lsb(T n){return n==0?-1:__builtin_ctzll(n);}
template<typename T>
constexpr std::enable_if_t<std::is_integral_v<T>,T>floor_pow2(T n){return n==0?0:T(1)<<msb(n);}
template<typename T>
constexpr std::enable_if_t<std::is_integral_v<T>,T>ceil_pow2(T n){return n<=1?1:T(1)<<(msb(n-1)+1);}
template<std::integral T>
constexpr T safe_div(T a,T b){return a/b-(a%b&&(a^b)<0);}
template<std::integral T>
constexpr T safe_ceil(T a,T b){return a/b+(a%b&&(a^b)>0);}
template<int m>
struct ntt_root{
static constexpr int rank2=lsb(m-1);
static constexpr int g=primitive_root_constexpr(m);
std::array<int,rank2+1>root,invroot;
std::array<int,std::max(0,rank2-1)>rate2,invrate2;
std::array<int,std::max(0,rank2-2)>rate3,invrate3;
constexpr ntt_root(){
root[rank2]=pow_mod(g,m>>rank2,m);
invroot[rank2]=pow_mod(root[rank2],m-2,m);
for(int i=rank2-1;i>=0;i--){
root[i]=(long long)root[i+1]*root[i+1]%m;
invroot[i]=(long long)invroot[i+1]*invroot[i+1]%m;
}
int prod=1,invprod=1;
for(int i=0;i<rank2-1;i++){
rate2[i]=(long long)root[i+2]*prod%m;
invrate2[i]=(long long)invroot[i+2]*invprod%m;
prod=(long long)prod*invroot[i+2]%m;
invprod=(long long)invprod*root[i+2]%m;
}
prod=invprod=1;
for(int i=0;i<rank2-2;i++){
rate3[i]=(long long)root[i+3]*prod%m;
invrate3[i]=(long long)invroot[i+3]*invprod%m;
prod=(long long)prod*invroot[i+3]%m;
invprod=(long long)invprod*root[i+3]%m;
}
}
};
template<typename T>
void dft(std::vector<T>&a){
static constexpr ntt_root<T::mod()>r;
static constexpr unsigned long long mod2=(unsigned long long)T::mod()*T::mod();
int n=a.size();
int h=lsb(n);
int len=0;
while(len<h){
if(h-len==1){
T rot=T::raw(1);
for(int s=0;s<(1<<len);s++){
int of=s*2;
T u=a[of],v=a[of+1]*rot;
a[of]=u+v;
a[of+1]=u-v;
rot*=T::raw(r.rate2[lsb(~(unsigned int)s)]);
}
len++;
}
else{
int p=1<<(h-len-2);
T rot=T::raw(1),imag=T::raw(r.root[2]);
for(int s=0;s<(1<<len);s++){
const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();
int of=s<<(h-len);
for(int i=0;i<p;i++){
const unsigned long long a0=a[i+of].val(),a1=(unsigned long long)a[i+of+p].val()*rot1,a2=(unsigned long long)a[i+of+p*2].val()*rot2,a3=(unsigned long long)a[i+of+p*3].val()*rot3;
const unsigned long long m=(unsigned long long)T(a1+mod2-a3).val()*imag.val();
const unsigned long long k=mod2-a2;
a[i+of]=a0+a2+a1+a3;
a[i+of+p]=a0+a2+(mod2*2-a1-a3);
a[i+of+p*2]=a0+k+m;
a[i+of+p*3]=a0+k+(mod2-m);
}
rot*=T::raw(r.rate3[lsb(~(unsigned int)s)]);
}
len+=2;
}
}
}
template<typename T>
void idft(std::vector<T>&a){
static constexpr ntt_root<T::mod()>r;
int n=a.size();
int h=lsb(n);
int len=h;
while(len){
if(len==1){
int p=1<<(h-1);
for(int i=0;i<p;i++){
T u=a[i],v=a[i+p];
a[i]=u+v;
a[i+p]=u-v;
}
len--;
}
else{
int p=1<<(h-len);
T rot=T::raw(1),imag=T::raw(r.invroot[2]);
for(int s=0;s<(1<<(len-2));s++){
const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();
int of=s<<(h-len+2);
for(int i=0;i<p;i++){
const unsigned long long a0=a[i+of].val(),a1=a[i+of+p].val(),a2=a[i+of+p*2].val(),a3=a[i+of+p*3].val();
const unsigned long long k=T((T::mod()+a2-a3)*imag.val()).val();
a[i+of]=a0+a1+a2+a3;
a[i+of+p]=(a0+T::mod()-a1+k)*rot1;
a[i+of+p*2]=(a0+a1+T::mod()*2-a2-a3)*rot2;
a[i+of+p*3]=(a0+T::mod()*2-a1-k)*rot3;
}
rot*=T::raw(r.invrate3[lsb(~(unsigned int)s)]);
}
len-=2;
}
}
}
template<typename T>
std::vector<T>ntt_convolution(std::vector<T> a,std::vector<T> b){
int n=a.size(),m=b.size(),s=n+m-1;
if(std::min(n,m)<60){
std::vector<T>ret(s,0);
if(n<m)for(int i=0;i<m;i++)for(int j=0;j<n;j++)ret[i+j]+=a[j]*b[i];
else for(int i=0;i<n;i++)for(int j=0;j<m;j++)ret[i+j]+=a[i]*b[j];
return ret;
}
int z=ceil_pow2(s);
a.resize(z,0);
b.resize(z,0);
dft(a),dft(b);
std::vector<T>c(z);
for(int i=0;i<z;i++)c[i]=a[i]*b[i];
idft(c);
T g=T::raw(z).inv();
for(int i=0;i<s;i++)c[i]*=g;
return {c.begin(),c.begin()+s};
}
template<typename T>
std::vector<std::vector<T>>convolution2d(const std::vector<std::vector<T>>&a,const std::vector<std::vector<T>>&b){
int x=a.size()+b.size()-1,y=a[0].size()+b[0].size()-1;
std::vector<T>f(a.size()*y),g(b.size()*y);
for(int i=0;i<a.size();i++)for(int j=0;j<a[i].size();j++)f[i*y+j]=a[i][j];
for(int i=0;i<b.size();i++)for(int j=0;j<b[i].size();j++)g[i*y+j]=b[i][j];
auto c=ntt_convolution(f,g);
std::vector<std::vector<T>>ret(x,std::vector<T>(y));
for(int i=0;i<x;i++)for(int j=0;j<y;j++)ret[i][j]=c[i*y+j];
return ret;
}
template<typename T>
std::vector<T> fps_inv(const std::vector<T> &a,int deg=-1){
int n=a.size();
if(deg==-1)deg=n;
const T zero=T::raw(0);
assert(a[0]!=zero);
std::vector<T> ret(ceil_pow2(deg));
ret[0]=a[0].inv();
for(int m=1;m<deg;m<<=1){
std::vector<T> f(a.begin(),a.begin()+std::min(n,m*2));
if(f.size()<m*2)f.resize(m*2,0);
std::vector<T> g(ret);
f.resize(m*2);
dft(f);
g.resize(m*2);
dft(g);
for(int i=0;i<m*2;i++)f[i]*=g[i];
idft(f);
T inv=T::raw(m*2).inv();
for(int i=0;i<m;i++)f[i]=zero;
for(int i=m;i<m*2;i++)f[i]*=inv;
dft(f);
for(int i=0;i<m*2;i++)f[i]*=g[i];
idft(f);
for(int i=0;i<m*2;i++)f[i]*=inv;
for(int i=m;i<m*2;i++)ret[i]-=f[i];
}
ret.resize(deg);
return ret;
}
template<typename T>
std::vector<T> fps_diff(const std::vector<T>&a){
int n=a.size();
std::vector<T>b(std::max(0,n-1));
for(int i=1;i<n;i++)b[i-1]=a[i]*T::raw(i);
return b;
}
template<typename T>
std::vector<T> fps_integral(const std::vector<T>&a){
int n=a.size();
std::vector<T>b(n+1);
b[0]=0;
if(n)b[1]=1;
for(int i=2;i<=n;i++)b[i]=-b[T::mod()%i]*(T::mod()/i);
for(int i=0;i<n;i++)b[i+1]*=a[i];
return b;
}
template<typename T>
std::vector<T> fps_log(const std::vector<T>&a,int deg=-1){
int n=a.size();
if(deg==-1)deg=n;
std::vector<T>b=fps_integral(ntt_convolution(fps_diff(a),fps_inv(a,deg)));
return {b.begin(),b.begin()+deg};
}
template<typename T>
std::vector<T> fps_exp(const std::vector<T>&a,int deg=-1){
assert(a.empty()||a[0]==0);
int n=a.size();
if(deg==-1)deg=n;
std::vector<T>inv(ceil_pow2(deg));
inv[0]=0,inv[1]=1;
for(int i=2;i<inv.size();i++)inv[i]=-inv[T::mod()%i]*(T::mod()/i);
std::vector<T>b{1,1<n?a[1]:T()},c{T::raw(1)},f1,f2(2,T::raw(1));
T sinv=T::raw(2).inv();
for(int m=2;m<deg;m*=2){
std::vector<T>y(b);
y.resize(m*2);
dft(y);
f1=f2;
std::vector<T>z(m);
for(int i=0;i<m;i++)z[i]=y[i]*f1[i];
idft(z);
for(int i=m/2;i<m;i++)z[i]*=sinv;
std::fill(z.begin(),z.begin()+m/2,T());
dft(z);
for(int i=0;i<m;i++)z[i]*=-f1[i];
idft(z);
for(int i=m/2;i<m;i++)z[i]*=sinv;
c.insert(c.end(),z.begin()+m/2,z.end());
f2=c;
f2.resize(m*2);
dft(f2);
std::vector<T>x(m);
std::copy(a.begin(),a.begin()+std::min(n,m),x.begin());
for(int i=0;i<m-1;i++)x[i]=x[i+1]*T::raw(i+1);
x.back()=T();
dft(x);
for(int i=0;i<m;i++)x[i]*=y[i];
idft(x);
for(int i=0;i<m;i++)x[i]*=sinv;
x.resize(m*2);
for(int i=0;i<m-1;i++)x[m+i]=x[i]-b[i+1]*T::raw(i+1),x[i]=T();
dft(x);
for(int i=0;i<m*2;i++)x[i]*=f2[i];
idft(x);
sinv/=2;
for(int i=0;i<m*2;i++)x[i]*=sinv;
for(int i=(int)x.size()-1;i>=1;i--)x[i]=x[i-1]*inv[i];
x[0]=T();
for(int i=m;i<std::min(n,m*2);i++)x[i]+=a[i];
std::fill(x.begin(),x.begin()+m,T());
dft(x);
for(int i=0;i<m*2;i++)x[i]*=y[i];
idft(x);
for(int i=m;i<m*2;i++)x[i]*=sinv;
b.insert(b.end(),x.begin()+m,x.end());
}
b.resize(deg);
return b;
}
template<typename T>
std::vector<T> fps_pow(std::vector<T> a,unsigned long long k,int deg=-1){
int n=a.size();
if(deg==-1)deg=n;
if(k==0){
std::vector<T>ret(deg,0);
ret[0]=1;
return ret;
}
int of=0;
while(a[of]==0&&of!=n)of++;
if(of==n)return std::vector<T>(deg,0);
if(of!=0&&k>=deg)return std::vector<T>(deg,0);
if(of*k>=deg)return std::vector<T>(deg,0);
a.erase(a.begin(),a.begin()+of);
n=a.size();
T a0=a[0];
T inv=a[0].inv();
for(int i=0;i<n;i++)a[i]*=inv;
std::vector<T>lg=fps_log(a,deg);
T tk=T(k);
for(int i=0;i<deg;i++)lg[i]*=tk;
std::vector<T>ep=fps_exp(lg,deg);
T pw=a0.pow(k);
for(int i=0;i<deg;i++)ep[i]*=pw;
std::vector<T>ret(deg,0);
for(int i=of*k;i<deg;i++)ret[i]=ep[i-of*k];
return ret;
}
template<typename T>
std::vector<T>fps_divmod(std::vector<T>f,std::vector<T>g){
if(f.empty())return f;
int n=f.size(),m=g.size();
std::vector<T>r(f);
std::reverse(f.begin(),f.end()),std::reverse(g.begin(),g.end());
std::vector<T>q=ntt_convolution(f,fps_inv(g,n));
q.resize(std::max(0,n-m+1));
auto p=ntt_convolution(g,q);
std::reverse(p.begin(),p.end());
for(int i=0;i<std::min<int>(p.size(),m);i++)r[i]-=p[i];
r.resize(m-1);
while(!r.empty()&&r.back().val()==0)r.pop_back();
return r;
}
template<typename T>
std::optional<std::vector<T>>fps_sqrt(std::vector<T>f,int deg=-1){
if(deg==-1)deg=f.size();
int prefix_zero=0;
while(prefix_zero<f.size()&&f[prefix_zero].val()==0)prefix_zero++;
if(prefix_zero==f.size())return std::make_optional(std::vector<T>(deg,0));
if(prefix_zero&1)return std::nullopt;
f.erase(f.begin(),f.begin()+prefix_zero);
prefix_zero/=2;
auto opt_sq=f[0].sqrt();
if(!opt_sq)return std::nullopt;
T sq=*opt_sq;
T inv0=f[0].inv();
for(int i=0;i<f.size();i++)f[i]*=inv0;
std::vector<T>g{1};
T inv2=T::raw(2).inv();
while(g.size()<deg-prefix_zero){
std::vector<T>fp(f.begin(),f.begin()+std::min(f.size(),g.size()*2));
fp=ntt_convolution(fp,fps_inv(g,g.size()*2));
std::vector<T>nxtg(g);
nxtg.resize(g.size()*2);
for(int i=0;i<nxtg.size();i++){
if(i<fp.size())nxtg[i]+=fp[i];
nxtg[i]*=inv2;
}
std::swap(g,nxtg);
}
g.insert(g.begin(),prefix_zero,0);
g.resize(deg);
for(int i=0;i<g.size();i++)g[i]*=sq;
return g;
}
template<typename T>
void ntt_doubling(std::vector<T>&a){
static constexpr ntt_root<T::mod()>r;
int n=a.size()/2;
std::vector<T>b(a.begin(),a.begin()+n);
idft(b);
T now=T::raw(n).inv(),zeta=T::raw(r.root[msb(n)+1]);
for(int i=0;i<n;i++){
b[i]*=now;
now*=zeta;
}
dft(b);
std::copy(b.begin(),b.end(),a.begin()+n);
}
//0≤j<mに対するsum(f_i*g_i^j)の列挙
template<typename T>
std::vector<T>power_prod_sum(std::vector<T>f,std::vector<T>g,int m){
assert(f.size()==g.size());
int s=f.size();
int n=ceil_pow2(f.size()),log2n=msb(n);
for(int i=0;i<s;i++)g[i]=-g[i];
f.resize(n),g.resize(n);
for(int i=0;i<log2n;i++){
int b=1<<i;
std::vector<T>lf(b*2),lg(b*2),rf(b*2),rg(b*2);
int j;
for(j=0;j+b<s;j+=b*2){
std::copy(f.begin()+j,f.begin()+j+b,lf.begin());
std::copy(f.begin()+j+b,f.begin()+j+b*2,rf.begin());
std::copy(g.begin()+j,g.begin()+j+b,lg.begin());
std::copy(g.begin()+j+b,g.begin()+j+b*2,rg.begin());
ntt_doubling(lf),ntt_doubling(rf),ntt_doubling(lg),ntt_doubling(rg);
for(int k=0;k<b;k++)lg[k]++,rg[k]++;
for(int k=b;k<b*2;k++)lg[k]--,rg[k]--;
for(int k=0;k<b*2;k++){
f[j+k]=lf[k]*rg[k]+lg[k]*rf[k];
g[j+k]=lg[k]*rg[k];
g[j+k]--;
}
}
if(j<s){
std::copy(f.begin()+j,f.begin()+j+b,lf.begin());
std::copy(g.begin()+j,g.begin()+j+b,lg.begin());
ntt_doubling(lf),ntt_doubling(lg);
for(int k=0;k<b;k++){
f[j+k]=lf[k];
g[j+k]=lg[k];
}
for(int k=b;k<b*2;k++){
f[j+k]=-lf[k];
g[j+k]=-lg[k];
}
}
}
idft(f),idft(g);
g.push_back(n);
std::reverse(f.begin(),f.end());
std::reverse(g.begin(),g.end());
f.resize(m),g.resize(m);
f=ntt_convolution(f,fps_inv(g));
f.resize(m);
return f;
}
constexpr int carmichael_constexpr(int n){
if(n==998244353)return 998244352;
if(n==1000000007)return 1000000006;
if(n<=1)return n;
int res=1;
int t=0;
while(n%2==0){
n/=2;
t++;
}
if(t==2)res=2;
else if(t>=3)res=1<<(t-2);
for(int i=3;i*i<=n;i++)if(n%i==0){
int c=0;
while(n%i==0){
n/=i;
c++;
}
int prod=i-1;
for(int j=0;j<c-1;j++)prod*=i;
res=std::lcm(res,prod);
}
if(n!=1)res=std::lcm(res,n-1);
return res;
}
template<int m>
struct mod_int{
private:
static constexpr unsigned int umod=static_cast<unsigned int>(m);
static constexpr unsigned int car=carmichael_constexpr(m);
using uint=unsigned int;
using mint=mod_int;
uint v;
static_assert(m<uint(1)<<31);
mint sqrt_impl()const{
if(this->val()<=1)return *this;
if constexpr(m%8==1){
mint b=2;
while(b.pow((m-1)/2).val()==1)b++;
int m2=m-1,e=0;
while(m2%2==0)m2>>=1,e++;
mint x=this->pow((m2-1)/2);
mint y=(*this)*x*x;
x*=*this;
mint z=b.pow(m2);
while(y.val()!=1){
int j=0;
mint t=y;
while(t.val()!=1)t*=t,j++;
z=z.pow(1<<(e-j-1));
x*=z;
z*=z;
y*=z;e=j;
}
return x;
}
else if constexpr(m%8==5){
mint ret=this->pow((m+3)/8);
if((ret*ret).val()==this->val())return ret;
else return ret*mint::raw(2).pow((m-1)/4);
}
else{
return this->pow((m+1)/4);
}
}
public:
using value_type=uint;
mod_int():v(0){}
template<typename T,std::enable_if_t<std::is_signed_v<T>,std::nullptr_t> =nullptr>
mod_int(T a){
a%=m;
if(a<0)v=a+umod;
else v=a;
}
template<typename T,std::enable_if_t<std::is_unsigned_v<T>,std::nullptr_t> =nullptr>
mod_int(T a):v(a%umod){}
static constexpr mint raw(int a){
mint ret;
ret.v=a;
return ret;
}
inline uint val()const{return this->v;}
static constexpr int mod(){return m;}
inline mint &operator+=(const mint &b){
this->v+=b.v;
if(this->v>=umod)this->v-=umod;
return *this;
}
inline mint &operator-=(const mint &b){
this->v-=b.v;
if(this->v>=umod)this->v+=umod;
return *this;
}
inline mint &operator*=(const mint &b){
this->v=((unsigned long long)this->v*b.v)%umod;
return *this;
}
inline mint &operator/=(const mint &b){
*this*=b.inv();
return *this;
}
inline mint operator+()const{return *this;}
inline mint operator-()const{return mint()-*this;}
friend inline mint operator+(const mint &a,const mint &b){return mint(a)+=b;}
friend inline mint operator-(const mint &a,const mint &b){return mint(a)-=b;}
friend inline mint operator*(const mint &a,const mint &b){return mint(a)*=b;}
friend inline mint operator/(const mint &a,const mint &b){return mint(a)/=b;}
friend inline bool operator==(const mint &a,const mint &b){return a.val()==b.val();}
friend inline bool operator!=(const mint &a,const mint &b){return !(a==b);}
inline mint operator++(int){
mint ret=*this;
*this+=mint::raw(1);
return ret;
}
inline mint operator--(int){
mint ret=*this;
*this-=mint::raw(1);
return ret;
}
mint pow(long long n)const{
mint ret=mint::raw(1),a(*this);
while(n){
if(n&1)ret*=a;
a*=a;
n>>=1;
}
return ret;
}
inline mint inv()const{
assert(this->v!=0);
return pow(car-1);
}
std::optional<mint>sqrt()const{
if(this->val()<=1||this->pow((m-1)/2)==1)return std::make_optional(this->sqrt_impl());
else return std::nullopt;
}
static constexpr unsigned int order(){return car;}
friend std::istream &operator>>(std::istream &is,mint &b){
long long a;
is>>a;
b=mint(a);
return is;
}
friend std::ostream &operator<<(std::ostream &os,const mint &b){
os<<b.val();
return os;
}
};
template<int m>
struct std::hash<mod_int<m>>{
std::size_t operator()(mod_int<m>x)const{
return std::hash<unsigned int>()(x.val());
}
};
using mint998=mod_int<998244353>;
using mint107=mod_int<1000000007>;
using mint=mint998;
using namespace std;
int main(){
int n,m;
cin>>n>>m;
vector<mint>a(n),b(n);
for(int i=0;i<n;i++){
a[i]=1;
cin>>b[i];
}
a=power_prod_sum(a,b,m+1);
for(int i=1;i<=m;i++)cout<<a[i]<<" \n"[i==m];
}