[模板]多项式封装(无讲解)

// luogu-judger-enable-o2
#include<bits/stdc++.h>
#define mod 998244353
#define G 3
#define Gi 332748118
using namespace std;
typedef long long int ll;
typedef long double ld;
const int maxn=4E5+5;
const double pi=std::acos(-1);
const ll K=32768;

ll n,a[maxn*2],wait[maxn*2],wait_val[maxn*2];
ll poly_A[maxn*2],poly_B[maxn*2];

int r[maxn*2];
template<class T>inline void copy(T*A,T*B,int n)
{
    for(int i=0;i<=n;++i)
        A[i]=B[i];
}
inline ll qpow(ll x,ll y)
{
    ll ans=1,base=x;
    while(y)
    {
        if(y&1)
            ans=ans*base%mod;
        base=base*base%mod;
        y>>=1;
    }
    return ans;
}
struct poly
{
    ll*f;
    int n;
    poly(int x)
    {
        n=x;
        f=new ll[n+1];
        for(int i=0;i<=n;++i)
            f[i]=0;
    }
    template<class T>poly(int x,T*A)
    {
        n=x;
        f=new ll[n+1];
        for(int i=0;i<=n;++i)
            wait_val[i]=A[i];
        for(int i=0;i<=n;++i)
            f[i]=wait_val[i];
    }
    void change(int x,bool keep=1)
    {
        if(keep)
            for(int i=0;i<=n;++i)
                wait[i]=f[i];
        delete f;
        f=new ll[x+1];
        for(int i=0;i<=x;++i)
            f[i]=0;
        if(keep)
            for(int i=0;i<=min(n,x);++i)
                f[i]=wait[i];
        n=x;
    }
    void DFT(int len,int sign,ll*g)
    {
        copy(wait,f,1<<len);
        for(int i=0;i<(1<<len);++i)
        {
            r[i]=(r[i>>1]>>1)|(i&1?1<<(len-1):0);
            if(i<r[i])
                swap(wait[i],wait[r[i]]);
        }
        for(int i=2;i<=(1<<len);i<<=1)
        {
            ll d;
            if(sign==1)
                d=qpow(G,(mod-1)/i);
            else
                d=qpow(Gi,(mod-1)/i);
            for(int j=0;j<(1<<len)/i;++j)
            {
                ll w=1;
                for(int k=0;k<i/2;++k)
                {
                    ll a=wait[j*i+k],b=wait[j*i+k+i/2]*w%mod;
                    wait[j*i+k]=(a+b)%mod;
                    wait[j*i+k+i/2]=(a-b+mod)%mod;
                    w=w*d%mod;
                }
            }
        }
        copy(g,wait,1<<len);
    }
    void integral()
    {
        change(n+1);
        for(int i=n;i>=1;--i)
            f[i]=f[i-1]*qpow(i,mod-2)%mod;
        f[0]=0;
    }
    void differential()
    {
        for(int i=0;i<n;++i)
            f[i]=(i+1)*f[i+1]%mod;
        f[n]=0;
    }
    void out()
    {
        for(int i=0;i<=n;++i)
            cout<<f[i]<<" ";
        cout<<endl;
    }
};
template<class T>static void FFT(poly&A,poly&B,T*to,bool show=0)
{
    int len=0,s=A.n+B.n,Bn=B.n;
    while((1<<len)<=A.n+B.n+1)
        ++len;
    int limit=1<<len;
    if(show)
        cout<<"NOW"<<len<<" "<<limit<<endl;
    if(show)
        cout<<"--------------------"<<endl;
    A.change(limit);
    B.change(limit);
    if(show)
        A.out(),B.out();
    if(show)
        cout<<"--------------------"<<endl;
    A.DFT(len,1,A.f);
    B.DFT(len,1,poly_B);
    for(int i=0;i<limit;++i)
        A.f[i]=A.f[i]*poly_B[i];
    A.DFT(len,-1,A.f);
    ll g=qpow(limit,mod-2);
    for(int i=0;i<limit;++i)
        to[i]=A.f[i]=A.f[i]*g%mod;
    A.change(s);
    B.change(Bn);
}
static void polyInv(const poly&A,poly&P,int now)
{
    if(now==0)
    {
        P.f[0]=qpow(A.f[0],mod-2);
        return;
    }
    polyInv(A,P,now>>1);
    poly B(now,A.f),B_(now>>1,P.f);
    FFT(B,B_,wait);
    B.change(now);
    FFT(B,B_,wait);
    for(int i=0;i<=now>>1;++i)
        P.f[i]=(2*P.f[i]-B.f[i]+mod)%mod;
    for(int i=(now>>1)+1;i<=now;++i)
        P.f[i]=(mod-B.f[i])%mod;
}
static void polyIn(poly&P)
{
    poly A(P.n,P.f),B(P.n);
    A.differential();
    polyInv(P,B,P.n);
    FFT(B,A,wait);
    P=B;
    P.integral();
    P.change(A.n);
}
static void polyExp(const poly&A,poly&P,int now)
{
    if(now==0)
    {
        P.f[0]=1;
        return;
    }
    polyExp(A,P,now>>1);
    poly F(now,P.f),H(now,P.f);
    for(int i=P.n+1;i<=now;++i)
        F.f[i]=H.f[i]=0;
    polyIn(H);
    for(int i=0;i<=now;++i)
        H.f[i]=((i==0)-H.f[i]+A.f[i]+mod)%mod;
    FFT(H,F,wait);
    P.change(now);
    copy(P.f,H.f,now);
}
static void polySqrt(poly&P)
{
    polyIn(P);
    ll g=qpow(2,mod-2);
    for(int i=0;i<=P.n;++i)
        P.f[i]=P.f[i]*g%mod;
    poly A(P.n,wait);
    polyExp(P,A,P.n);
    copy(P.f,A.f,P.n);
}
static void polyPow(poly&P,ll k)
{
    polyIn(P);
    for(int i=0;i<=P.n;++i)
        P.f[i]=P.f[i]*k%mod;
    poly A(P.n,wait);
    polyExp(P,A,P.n);
    copy(P.f,A.f,P.n);
}
int main()
{
    ios::sync_with_stdio(false);
    string str;
    ll k=0;
    cin>>n>>str;
    for(int i=0;i<str.size();++i)
        k=(k*10+str[i]-'0')%mod;
    --n;
    for(int i=0;i<=n;++i)
        cin>>a[i];
    poly A(n,a);
    polyPow(A,k);
    A.out();
    return 0;
}