結果
| 問題 | No.3620 Compositional Power with Schröder Coordinate 2 |
| コンテスト | |
| ユーザー |
 Taiki0715
|
| 提出日時 | 2026-08-10 21:44:00 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.90.0) |
| 結果 |
AC
|
| 実行時間 | 1,716 ms / 10,000 ms |
| + 975µs | |
| コード長 | 29,705 bytes |
| 記録 | |
| コンパイル時間 | 3,123 ms |
| コンパイル使用メモリ | 361,076 KB |
| 実行使用メモリ | 58,688 KB |
| 最終ジャッジ日時 | 2026-08-10 23:59:54 |
| 合計ジャッジ時間 | 13,168 ms |
|
ジャッジサーバーID （参考情報） |
judge1_0 / judge3_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 7 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using ull=unsigned long long;
using P=pair<ll,ll>;
template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;
template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}
template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}
template<typename T1,typename T2>istream &operator>>(istream &is,pair<T1,T2>&p){is>>p.first>>p.second;return is;}
template<typename T1,typename T2,typename T3>istream &operator>>(istream &is,tuple<T1,T2,T3>&a){is>>std::get<0>(a)>>std::get<1>(a)>>std::get<2>(a);return is;}
template<typename T,size_t n>istream &operator>>(istream &is,array<T,n>&a){for(auto&i:a)is>>i;return is;}
template<typename T>istream &operator>>(istream &is,vector<T> &a){for(auto &i:a)is>>i;return is;}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int n){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int n){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int n){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int n){for(auto &i:a)i--;}
#define overload3(_1,_2,_3,name,...) name
#define rep1(i,n) for(int i=0;i<(int)(n);i++)
#define rep2(i,l,r) for(int i=(int)(l);i<(int)(r);i++)
#define rep(...) overload3(__VA_ARGS__,rep2,rep1)(__VA_ARGS__)
#define reps(i,l,r) rep2(i,l,r)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcountll(x)
#define fin(x) return cout<<(x)<<'\n',static_cast<void>(0)
#define yn(x) cout<<((x)?"Yes\n":"No\n")
#define uniq(x) sort(all(x)),x.erase(unique(all(x)),x.end())
template<typename T>
inline int fkey(vector<T>&z,T key){return lower_bound(z.begin(),z.end(),key)-z.begin();}
ll myceil(ll a,ll b){return (a+b-1)/b;}
template<typename T,size_t n,size_t id=0>
auto vec(const int (&d)[n],const T &init=T()){
if constexpr (id<n)return vector(d[id],vec<T,n,id+1>(d,init));
else return init;
}
#ifdef LOCAL
#include<debug.h>
#define SWITCH(a,b) (a)
#else
#define debug(...) static_cast<void>(0)
#define debugg(...) static_cast<void>(0)
#define SWITCH(a,b) (b)
template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}
#endif
struct Timer{
clock_t start;
Timer(){
start=clock();
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout<<fixed<<setprecision(16);
}
inline double now(){return (double)(clock()-start)/1000;}
#ifdef LOCAL
~Timer(){
cerr<<"time:";
cerr<<now();
cerr<<"ms\n";
}
#endif
}timer;
void SOLVE();
int main(){
int testcase=1;
//cin>>testcase;
for(int i=0;i<testcase;i++){
SOLVE();
}
}
#include<initializer_list>
constexpr bool isprime_constexpr(unsigned long long n){
if(n==998244353)return true;
if(n==1000000007)return true;
if(n<64)return 2891462833508853932ll>>n&1;
if(n%2==0)return false;
unsigned long long d=n-1;
int s=0;
while(!(d&1))d>>=1,s++;
int q=63;
while(!(d>>q))q--;
unsigned long long r=n;
for(int i=0;i<5;i++)r*=2-r*n;
auto redc=[&r,&n](__uint128_t x)->unsigned long long {
x=(x+__uint128_t((unsigned long long)x*-r)*n)>>64;
return x>=n?x-n:x;
};
__uint128_t r2=-__uint128_t(n)%n;
unsigned long long one=redc(r2);
for(unsigned long long base:{2,325,9375,28178,450775,9780504,1795265022}){
if(base%n==0)continue;
unsigned long long a=base=redc((base%n)*r2);
for(int i=q-1;i>=0;i--){
a=redc(__uint128_t(a)*a);
if(d>>i&1)a=redc(__uint128_t(a)*base);
}
if(a==one)continue;
for(int i=1;a!=n-one;i++){
if(i>=s)return false;
a=redc(__uint128_t(a)*a);
}
}
return true;
}
constexpr int factorize_constexpr(unsigned long long n,unsigned long long*a){
if(n<=1)return 0;
int ptr=0;
while(n%2==0){
a[ptr++]=2;
n/=2;
}
while(n>1){
if(isprime_constexpr(n)){
a[ptr++]=n;
break;
}
unsigned long long pf=n;
unsigned long long x=0,y=0;
int c=1;
do{
x=((__uint128_t)x*x+c)%pf;
y=((__uint128_t)y*y+c)%pf;
y=((__uint128_t)y*y+c)%pf;
unsigned long long g=std::gcd(x>y?x-y:y-x,pf);
if(g==pf){
c++;
x=y=0;
continue;
}
if(g>1)pf=g;
}while(!isprime_constexpr(pf));
while(n%pf==0){
a[ptr++]=pf;
n/=pf;
}
}
return ptr;
}
#include<type_traits>
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);
}
namespace Random{
constexpr unsigned long long to_seed(const char*s){
unsigned long long h=14695981039346656037ULL;
while(*s){
h^=static_cast<unsigned char>(*s++);
h*=1099511628211ULL;
}
return h;
}
constexpr unsigned long long constexpr_random_seed=(to_seed(__TIME__)*0x9e3779b97f4a7c15ULL)^to_seed(__DATE__);
constexpr unsigned long long next_value(unsigned long long n){
n^=n<<13;
n^=n>>7;
n^=n<<17;
return n;
}
}
constexpr unsigned long long primitive_root_constexpr(unsigned long long x){
if(!isprime_constexpr(x))throw "not prime";
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;
unsigned long long a[64]={};
int ptr=factorize_constexpr(x-1,a);
for(unsigned long long v=Random::constexpr_random_seed;;){
unsigned long long g=v%(x-1)+1;
bool ok=true;
for(int i=0;i<ptr;i++){
if(i>0&&a[i-1]==a[i])continue;
if(pow_mod<unsigned long long>(g,(x-1)/a[i],x)==1){
ok=false;
break;
}
}
if(ok)return g;
v=Random::next_value(v);
}
}
#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<auto m>
struct ntt_root{
static_assert(1<=m&&m<(1ull<<63));
static_assert(isprime_constexpr(m));
using value_type=std::conditional_t<((m>>31)==0),uint32_t,uint64_t>;
using mul_type=std::conditional_t<((m>>31)==0),uint64_t,__uint128_t>;
static constexpr int rank2=lsb(m-1);
static constexpr value_type g=primitive_root_constexpr(m);
std::array<value_type,rank2+1>root,invroot;
std::array<value_type,std::max(0,rank2-1)>rate2,invrate2;
std::array<value_type,std::max(0,rank2-2)>rate3,invrate3;
constexpr ntt_root(){
root[rank2]=pow_mod<value_type>(g,m>>rank2,m);
invroot[rank2]=pow_mod<value_type>(root[rank2],m-2,m);
for(int i=rank2-1;i>=0;i--){
root[i]=(mul_type)root[i+1]*root[i+1]%m;
invroot[i]=(mul_type)invroot[i+1]*invroot[i+1]%m;
}
value_type prod=1,invprod=1;
for(int i=0;i<rank2-1;i++){
rate2[i]=(mul_type)root[i+2]*prod%m;
invrate2[i]=(mul_type)invroot[i+2]*invprod%m;
prod=(mul_type)prod*invroot[i+2]%m;
invprod=(mul_type)invprod*root[i+2]%m;
}
prod=invprod=1;
for(int i=0;i<rank2-2;i++){
rate3[i]=(mul_type)root[i+3]*prod%m;
invrate3[i]=(mul_type)invroot[i+3]*invprod%m;
prod=(mul_type)prod*invroot[i+3]%m;
invprod=(mul_type)invprod*root[i+3]%m;
}
}
};
template<typename T>
void dft(std::vector<T>&a){
using value_type=typename T::value_type;
using mul_type=typename T::mul_type;
#ifdef NTT_SIMD
if constexpr(std::numeric_limits<value_type>::digits<=32){
if((int)a.size()>=32){
dft_simd(a);
return;
}
}
#endif
static constexpr ntt_root<T::mod()>r;
static constexpr mul_type mod2=(mul_type)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 mul_type rot1=rot.val(),rot2=(rot*rot).val(),rot3=(rot*T::raw(rot2)).val();
int of=s<<(h-len);
for(int i=0;i<p;i++){
const mul_type a0=a[i+of].val(),a1=(mul_type)a[i+of+p].val()*rot1,a2=(mul_type)a[i+of+p*2].val()*rot2,a3=(mul_type)a[i+of+p*3].val()*rot3;
const mul_type m=(mul_type)T(a1+mod2-a3).val()*imag.val();
const mul_type 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){
using value_type=typename T::value_type;
using mul_type=typename T::mul_type;
#ifdef NTT_SIMD
if constexpr(std::numeric_limits<value_type>::digits<=32){
if((int)a.size()>=32){
idft_simd(a);
return;
}
}
#endif
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 mul_type rot1=rot.val(),rot2=(rot*rot).val(),rot3=(rot*T::raw(rot2)).val();
int of=s<<(h-len+2);
for(int i=0;i<p;i++){
const mul_type 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 mul_type 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){
if(n==0||m==0)return {};
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<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>power_projection(const std::vector<T>&f,const std::vector<T>&g,int m){
assert(f.size()==g.size());
const int n=ceil_pow2(f.size());
std::vector<T>p(n*4),q(n*4);
std::vector<T>prep(n*4),preq(n*4);
T invn4=T(n*4).inv();
for(int i=0;i<(int)f.size();i++)p[i+n-f.size()]=g[i],q[i]=-f[i];
for(int x=n,y=1;x>1;x>>=1,y<<=1){
std::copy(p.begin(),p.begin()+n*2,prep.begin());
std::copy(q.begin(),q.begin()+n*2,preq.begin());
dft(p),dft(q);
for(int i=0;i<n*2;i++){
T l=q[i*2],r=q[i*2+1];
p[i*2]*=r,p[i*2+1]*=l;
q[i*2]*=r,q[i*2+1]*=l;
}
idft(p),idft(q);
for(int i=0;i<n*4;i++)p[i]*=invn4,q[i]*=invn4;
for(int i=0;i<n*2;i++){
p[n*2+i]+=prep[i];
if(i%2==0)q[n*2+i]+=preq[i]+preq[i];
}
std::fill(prep.begin(),prep.end(),T()),std::fill(preq.begin(),preq.end(),T());
for(int j=0;j<y*2;j++)for(int i=0;i<x/2;i++){
prep[j*x+i]=p[j*x*2+i*2+1];
preq[j*x+i]=q[j*x*2+i*2];
}
std::swap(p,prep);
std::swap(q,preq);
}
for(int i=0;i<n;i++)p[i]=p[i*2],q[i]=q[i*2];
p.resize(n),q.resize(n+1);
q[n]=1;
std::reverse(p.begin(),p.end()),std::reverse(q.begin(),q.end());
p=ntt_convolution(p,fps_inv(q,m));
p.resize(m);
return p;
}
template<typename T>
void transposed_dft(std::vector<T>&a){
using value_type=typename T::value_type;
using mul_type=typename T::mul_type;
#ifdef NTT_SIMD
if constexpr(std::numeric_limits<value_type>::digits<=32){
if((int)a.size()>=32){
transposed_dft_simd(a);
return;
}
}
#endif
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.root[2]);
for(int s=0;s<(1<<(len-2));s++){
const mul_type rot1=rot.val(),rot2=(rot*rot).val(),rot3=(rot*T::raw(rot2)).val();
int of=s<<(h-len+2);
for(int i=0;i<p;i++){
const mul_type 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 mul_type 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;
}
if(s+1!=1<<(len-2))rot*=T::raw(r.rate3[lsb(~(unsigned int)s)]);
}
len-=2;
}
}
}
template<typename T>
void transposed_idft(std::vector<T>&a){
using value_type=typename T::value_type;
using mul_type=typename T::mul_type;
#ifdef NTT_SIMD
if constexpr(std::numeric_limits<value_type>::digits<=32){
if((int)a.size()>=32){
transposed_idft_simd(a);
return;
}
}
#endif
static constexpr ntt_root<T::mod()>r;
static constexpr mul_type mod2=(mul_type)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;
if(s+1!=1<<len)rot*=T::raw(r.invrate2[lsb(~(unsigned int)s)]);
}
len++;
}
else{
int p=1<<(h-len-2);
T rot=T::raw(1),imag=T::raw(r.invroot[2]);
for(int s=0;s<(1<<len);s++){
const mul_type rot1=rot.val(),rot2=(rot*rot).val(),rot3=(rot*T::raw(rot2)).val();
int of=s<<(h-len);
for(int i=0;i<p;i++){
const mul_type a0=a[i+of].val(),a1=(mul_type)a[i+of+p].val()*rot1,a2=(mul_type)a[i+of+p*2].val()*rot2,a3=(mul_type)a[i+of+p*3].val()*rot3;
const mul_type m=(mul_type)T(a1+mod2-a3).val()*imag.val();
const mul_type 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);
}
if(s+1!=1<<len)rot*=T::raw(r.invrate3[lsb(~(unsigned int)s)]);
}
len+=2;
}
}
}
template<typename T>
std::vector<T>transposed_ntt_convolution(std::vector<T>a,std::vector<T>b){
assert(a.size()>=b.size());
int n=a.size(),m=b.size();
int s=ceil_pow2(n);
T inv=T(s).inv();
for(int i=0;i<n;i++)a[i]*=inv;
a.resize(s),b.resize(s);
transposed_idft(a);
dft(b);
for(int i=0;i<s;i++)a[i]*=b[i];
transposed_dft(a);
a.resize(n-m+1);
return a;
}
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);
}
template<typename T>
void transposed_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);
a=std::vector<T>(a.begin()+n,a.end());
transposed_dft(a);
T now=T::raw(n).inv(),zeta=T::raw(r.root[msb(n)+1]);
for(int i=0;i<n;i++)a[i]*=now,now*=zeta;
transposed_idft(a);
for(int i=0;i<n;i++)a[i]+=b[i];
}
#include<optional>
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_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_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>
std::vector<T>multipoint_evaluation(std::vector<T>f,const std::vector<T>&x){
int n=ceil_pow2((int)x.size()),log2n=msb(n);
std::vector<std::vector<T>>f2(log2n+1,std::vector<T>(n*2));
for(int i=0;i<x.size();i++)f2[0][i*2]=-x[i];
for(int i=0;i<log2n;i++){
int b=1<<i;
std::vector<T>l(b*2),r(b*2);
for(int j=0;j<n*2;j+=b*4){
std::copy(f2[i].begin()+j,f2[i].begin()+j+b,l.begin());
std::copy(f2[i].begin()+j+b*2,f2[i].begin()+j+b*3,r.begin());
ntt_doubling(l),ntt_doubling(r);
for(int k=0;k<b;k++)l[k]++,r[k]++;
for(int k=b;k<b*2;k++)l[k]--,r[k]--;
std::copy(l.begin(),l.end(),f2[i].begin()+j);
std::copy(r.begin(),r.end(),f2[i].begin()+j+b*2);
for(int k=0;k<b*2;k++)f2[i+1][j+k]=l[k]*r[k]-T::raw(1);
}
}
std::vector<T>g(f2[log2n].begin(),f2[log2n].begin()+n);
idft(g);
{
T inv=T::raw(g.size()).inv();
for(int i=0;i<n;i++)g[i]*=inv;
}
g.push_back(T::raw(1));
std::reverse(g.begin(),g.end());
g=fps_inv(g,f.size());
f.resize(f.size()+n-1);
f=transposed_ntt_convolution(f,g);
std::reverse(f.begin(),f.end());
transposed_idft(f);
{
T inv=T::raw(f.size()).inv();
for(int i=0;i<f.size();i++)f[i]*=inv;
}
for(int i=log2n-1;i>=0;i--){
std::vector<T>nxtf(n);
int b=1<<i;
for(int j=0;j<n;j+=b*2){
std::vector<T>l(b*2),r(b*2);
for(int k=0;k<b*2;k++)l[k]=f[j+k]*f2[i][j*2+b*2+k],r[k]=f[j+k]*f2[i][j*2+k];
transposed_ntt_doubling(l),transposed_ntt_doubling(r);
for(int k=0;k<b;k++)nxtf[j+k]=l[k],nxtf[j+b+k]=r[k];
}
std::swap(f,nxtf);
}
f.resize(x.size());
return f;
}
constexpr std::pair<long long,long long>ext_gcd(long long a,long long b){
if(b==0)return std::make_pair(1,0);
auto [x,y]=ext_gcd(b,a%b);
std::swap(x,y);
return std::make_pair(x,y-a/b*x);
}
template<std::signed_integral T>
constexpr std::pair<T,T> inv_mod(T a,T b){
a%=b;
if(a<0)a+=b;
if(a==0)return std::make_pair(b,0);
T s=b,t=a;
T m0=0,m1=1;
while(t){
T u=s/t;
s-=t*u;
m0-=m1*u;
std::swap(s,t);
std::swap(m0,m1);
}
if(m0<0)m0+=b/s;
return std::make_pair(s,m0);
}
template<auto m>
struct modint{
static_assert(1<=m&&m<(1ull<<63));
using value_type=std::conditional_t<((m>>31)==0),uint32_t,uint64_t>;
using mul_type=std::conditional_t<((m>>31)==0),uint64_t,__uint128_t>;
private:
value_type v;
static constexpr value_type umod=m;
constexpr modint sqrt_impl()const{
if(this->val()<=1)return *this;
if(umod%8==1){
modint b=2;
while(b.pow((umod-1)/2).val()==1)b++;
value_type m2=umod-1;
int e=0;
while(m2%2==0)m2>>=1,e++;
modint x=this->pow((m2-1)/2);
modint y=(*this)*x*x;
x*=*this;
modint z=b.pow(m2);
while(y.val()!=1){
int j=0;
modint t=y;
while(t.val()!=1)t*=t,j++;
z=z.pow((value_type(1))<<(e-j-1));
x*=z;
z*=z;
y*=z;
e=j;
}
return x;
}
else if(umod%8==5){
modint res=this->pow((umod+3)/8);
if((res*res).val()==this->val())return res;
else return res*modint(2).pow((umod-1)/4);
}
else return this->pow((umod+1)/4);
}
template<typename U,std::enable_if_t<std::unsigned_integral<U>||std::is_same_v<U,__uint128_t>,std::nullptr_t> =nullptr>
static constexpr value_type take_mod(U x){
if constexpr(std::numeric_limits<U>::max()<umod)return x;
if constexpr(umod==(1ull<<61)-1){
value_type res=(x>>61)+(x&umod);
if(res>=umod)res-=umod;
return res;
}
if constexpr(umod==(1ull<<61)-(1ull<<24)+1){
static constexpr value_type mask=(1ull<<61)-1;
value_type high=x>>61,low=x&mask;
mul_type t=low+(mul_type(high)<<24)-high;
high=t>>61,low=t&mask;
low=low+(mul_type(high)<<24)-high;
if(low>=umod)low-=umod;
return low;
}
return x%umod;
}
public:
constexpr modint():v(0){}
template<typename U,std::enable_if_t<std::signed_integral<U>||std::is_same_v<U,__int128_t>,std::nullptr_t> =nullptr>
constexpr modint(U x){
x%=std::make_signed_t<value_type>(umod);
v=x>=0?x:x+umod;
}
template<typename U,std::enable_if_t<std::unsigned_integral<U>||std::is_same_v<U,__uint128_t>,std::nullptr_t> =nullptr>
constexpr modint(U x):v(take_mod<U>(x)){}
static constexpr value_type mod(){return umod;}
template<typename U>
static constexpr modint raw(U x){
modint res;
res.v=x;
return res;
}
constexpr std::make_signed_t<value_type> val()const{return v;}
constexpr modint &operator+=(const modint&b){
this->v+=b.v;
if(this->v>=umod)this->v-=umod;
return *this;
}
constexpr modint &operator-=(const modint&b){
this->v-=b.v;
if(this->v>=umod)this->v+=umod;
return *this;
}
constexpr modint &operator*=(const modint&b){
this->v=take_mod(mul_type(this->v)*mul_type(b.v));
return *this;
}
constexpr modint &operator/=(const modint&b){return *this*=b.inv();}
constexpr modint operator+()const{return *this;}
constexpr modint operator-()const{return modint()-*this;}
friend constexpr modint operator+(const modint&a,const modint&b){return modint(a)+=b;}
friend constexpr modint operator-(const modint&a,const modint&b){return modint(a)-=b;}
friend constexpr modint operator*(const modint&a,const modint&b){return modint(a)*=b;}
friend constexpr modint operator/(const modint&a,const modint&b){return modint(a)/=b;}
constexpr auto operator<=>(const modint&)const=default;
constexpr modint operator++(int){
modint res=*this;
this->v++;
if(this->v==umod)this->v=0;
return res;
}
constexpr modint operator--(int){
modint res=*this;
if(this->v==0)this->v=umod;
this->v--;
return res;
}
template<std::integral U>
constexpr modint pow(U k)const{
if constexpr(std::is_signed_v<U>){
assert(0<=k);
}
modint res=1,a(*this);
while(k){
if(k&1)res*=a;
a*=a;
k>>=1;
}
return res;
}
constexpr modint inv()const{
if constexpr(isprime_constexpr(umod)){
if(std::is_constant_evaluated()){
if(v==0){
throw "no inverse";
}
}
else assert(v!=0);
return pow(umod-2);
}
else{
modint res;
auto [g,x]=inv_mod<std::make_signed_t<value_type>>(this->v,umod);
if(std::is_constant_evaluated()){
if(g!=1){
throw "no inverse";
}
}
else assert(g==1);
res.v=x;
return res;
}
}
std::optional<modint>sqrt()const{
if(this->val()<=1||this->pow((umod-1)/2)==1)return std::make_optional(this->sqrt_impl());
else return std::nullopt;
}
friend std::istream &operator>>(std::istream&is,modint&b){
long long a;
is>>a;
b=modint(a);
return is;
}
friend std::ostream &operator<<(std::ostream&os,const modint&b){
os<<b.val();
return os;
}
};
template<auto m>
struct std::hash<modint<m>>{
std::size_t operator()(modint<m>x)const{
return std::hash<typename modint<m>::value_type>(x.val());
}
};
using mint998=modint<998244353>;
using mint107=modint<1000000007>;
using mint61=modint<2305843009213693951>;
using mint6124=modint<2305843009196916737>;
using mint=mint998;
void SOLVE(){
int n,m;
cin>>n>>m;
vector<mint>f(n),g(n),h(n);
cin>>f>>g>>h;
vector<mint>one(n);
one[0]=1;
auto g2=power_projection(g,one,n);
debug(g2);
rep(i,n)g2[i]*=h[i];
vector<mint>x(m);
rep(i,m)x[i]=f[1].pow(i);
auto ans=multipoint_evaluation(g2,x);
rep(i,m)cout<<ans[i]<<" \n"[i+1==m];
}