Luogu4512 【模板】多项式除法（多项式求逆+NTT）

　　http://blog.miskcoo.com/2015/05/polynomial-division 好神啊！

　　通过翻转多项式消除余数的影响，主要原理是商只与次数不小于m的项有关。

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int read()
{
    int x=,f=;char c=getchar();
    while (c<''||c>'') {if (c=='-') f=-;c=getchar();}
    while (c>=''&&c<='') x=(x<<)+(x<<)+(c^),c=getchar();
    return x*f;
}
#define N 550000
#define P 998244353
int n,m,t,a[N],b[N],r[N],c[N],d[N],e[N],inv3;
int ksm(int a,int k)
{
    if (k==) return ;
    int tmp=ksm(a,k>>);
    if (k&) return 1ll*tmp*tmp%P*a%P;
    else return 1ll*tmp*tmp%P;
}
int inv(int a){return ksm(a,P-);}
void DFT(int n,int *a,int p)
{
    for (int i=;i<n;i++) if (i<r[i]) swap(a[i],a[r[i]]);
    for (int i=;i<=n;i<<=)
    {
        int wn=ksm(p,(P-)/i);
        for (int j=;j<n;j+=i)
        {
            int w=;
            for (int k=j;k<j+(i>>);k++,w=1ll*w*wn%P)
            {
                int x=a[k],y=1ll*w*a[k+(i>>)]%P;
                a[k]=(x+y)%P,a[k+(i>>)]=(x-y+P)%P;
            }
        }
    }
}
void mul(int n,int *a,int *b)
{
    DFT(n,a,),DFT(n,b,);
    for (int i=;i<n;i++) a[i]=1ll*a[i]*b[i]%P;
    DFT(n,a,inv3);
    int invn=inv(n);
    for (int i=;i<n;i++) a[i]=1ll*a[i]*invn%P;
}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("division.in","r",stdin);
    freopen("division.out","w",stdout);
    const char LL[]="%I64d";
#else
    const char LL[]="%lld";
#endif
    n=read(),m=read();
    for (int i=;i<=n;i++) a[i]=read();
    for (int i=;i<=m;i++) b[i]=read();
    reverse(b,b+m+);
    t=;c[]=inv(b[]);
    inv3=inv();
    while (t<n-m+)
    {
        t<<=;
        for (int i=;i<t;i++) d[i]=b[i];
        t<<=;
        for (int i=;i<t;i++) r[i]=(r[i>>]>>)|(i&)*(t>>);
        memcpy(e,c,sizeof(e));
        mul(t,e,d);
        for (int i=;i<t;i++) e[i]=(P-e[i])%P;
        e[]=(e[]+)%P;
        for (int i=(t>>);i<t;i++) e[i]=;
        mul(t,c,e);
        for (int i=(t>>);i<t;i++) c[i]=;
        t>>=;
    }
    memcpy(d,a,sizeof(a));
    reverse(d,d+n+);
    for (int i=n-m+;i<=n;i++) c[i]=d[i]=;
    t=;while (t<=(n-m+<<)) t<<=;
    for (int i=;i<t;i++) r[i]=(r[i>>]>>)|(i&)*(t>>);
    mul(t,c,d);
    for (int i=n-m+;i<t;i++) c[i]=;
    reverse(c,c+n-m+);
    for (int i=;i<=n-m;i++) printf("%d ",c[i]);cout<<endl;
    reverse(b,b+m+);
    t=;while (t<=n) t<<=;
    for (int i=;i<t;i++) r[i]=(r[i>>]>>)|(i&)*(t>>);
    mul(t,c,b);
    for (int i=;i<m;i++) printf("%d ",(a[i]-c[i]+P)%P);
    return ;
}