poly

曾经的板子

DIF-DIT 版：

#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ull unsigned long long
using namespace std;
inline int read()
{
	char c=getchar();int x=0;bool f=0;
	for(;!isdigit(c);c=getchar())f^=!(c^45);
	for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
	if(f)x=-x;return x;
}
 
#define mod 998244353
struct modint{
	int x;
	modint(int o=0){x=o;}
	modint &operator = (int o){return x=o,*this;}
	modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
	modint &operator -=(modint o){return x=x-o.x<0?x-o.x+mod:x-o.x,*this;}
	modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
	modint &operator ^=(int b){
		modint a=*this,c=1;
		for(;b;b>>=1,a*=a)if(b&1)c*=a;
		return x=c.x,*this;
	}
	modint &operator /=(modint o){return *this *=o^=mod-2;}
	friend modint operator +(modint a,modint b){return a+=b;}
	friend modint operator -(modint a,modint b){return a-=b;}
	friend modint operator *(modint a,modint b){return a*=b;}
	friend modint operator /(modint a,modint b){return a/=b;}
	friend modint operator ^(modint a,int b){return a^=b;}
	friend bool operator ==(modint a,modint b){return a.x==b.x;}
	friend bool operator !=(modint a,modint b){return a.x!=b.x;}
	bool operator ! () {return !x;}
	modint operator - () {return x?mod-x:0;}
	bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}

vector<modint> fac,ifac,iv;
inline void initC(int n)
{
	if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
	int m=iv.size(); ++n;
	if(m>=n)return;
	iv.resize(n),fac.resize(n),ifac.resize(n);
	For(i,m,n-1){
		iv[i]=iv[mod%i]*(mod-mod/i);
		fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
	}
}
inline modint C(int n,int m){
	if(m<0||n<m)return 0;
	return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;

#define poly vector<modint>
const modint G=3,Ginv=modint(1)/3;
inline poly one(){poly a;a.push_back(1);return a;}
vector<int>rev;
int rts[2100000];
inline int ext(int n){
	int k=0;
	while((1<<k)<n)++k;return k; 
}
inline void init(int k){
	int n=1<<k;
	rts[0]=1,rts[1<<k]=qpow(31,1<<(21-k)).x;
	Rep(i,k,1)rts[1<<(i-1)]=1ull*rts[1<<i]*rts[1<<i]%mod;
	For(i,1,n-1)rts[i]=1ull*rts[i&(i-1)]*rts[i&-i]%mod;
}

void ntt(poly&a,int k,int typ){
	int n=1<<k;
	static ull tmp[2100000];
	for(int i=0;i<n;++i)tmp[i]=a[i].x;
	if(typ==1){
		for(int l=n>>1;l>=1;l>>=1){
			ull*k=tmp;
			for(int*g=rts;k<tmp+n;k+=(l<<1),++g){
				for(ull*x=k;x<k+l;++x){
					int o=x[l]%mod*(*g)%mod;
					x[l]=*x+mod-o,*x+=o;
				}
			}
		}
		for(int i=0;i<n;++i)a[i].x=tmp[i]%mod;
	}else{
		for(int l=1;l<n;l<<=1){
			ull*k=tmp;
			for(int*g=rts;k<tmp+n;k+=(l<<1),++g){
				for(ull*x=k;x<k+l;++x){
					int o=x[l]%mod;
					x[l]=(*x+mod-o)*(*g)%mod,*x+=o;
				}
			}
		}
		int iv=qpow(n,mod-2).x;
		for(int i=0;i<n;++i)a[i].x=tmp[i]%mod*iv%mod;
		reverse(a.begin()+1,a.end());
	}
}
 
poly operator +(poly a,poly b){
	int n=max(a.size(),b.size());a.resize(n),b.resize(n);
	For(i,0,n-1)a[i]+=b[i];return a;
}
poly operator -(poly a,poly b){
	int n=max(a.size(),b.size());a.resize(n),b.resize(n);
	For(i,0,n-1)a[i]-=b[i];return a;
}
poly operator *(poly a,modint b){
	int n=a.size();
	For(i,0,n-1)a[i]*=b;return a;
} 
poly operator *(poly a,poly b){
	if(!a.size()||!b.size())return {};
	if((int)a.size()<=32 || (int)b.size()<=32){
		poly c(a.size()+b.size()-1,0);
		for(int i=0;i<a.size();++i)for(int j=0;j<b.size();++j)c[i+j]+=a[i]*b[j];
		return c; 
	}
	int n=(int)a.size()+(int)b.size()-1,k=ext(n);
	a.resize(1<<k),b.resize(1<<k);
	ntt(a,k,1),ntt(b,k,1);
	For(i,0,(1<<k)-1)a[i]*=b[i];
	ntt(a,k,-1),a.resize(n);return a;
}

poly Tmp;
poly pmul(poly a,poly b,int n,bool ok=0)
{
	int k=ext(n);
	a.resize(1<<k),ntt(a,k,1);
	if(!ok) b.resize(1<<k),ntt(b,k,1),Tmp=b;
	For(i,0,(1<<k)-1)a[i]*=Tmp[i];
	ntt(a,k,-1),a.resize(n);
	return a;
}
poly inv(poly a,int n)
{
	a.resize(n);
	if(n==1){
		poly f(1,1/a[0]);
		return f;
	}
	poly f0=inv(a,(n+1)>>1),f=f0;
	poly now=pmul(a,f0,n,0);
	for(int i=0;i<f0.size();++i)now[i]=0;
	now=pmul(now,poly(0),n,1);
	f.resize(n);
	for(int i=f0.size();i<n;++i)f[i]=-now[i];
	return f;
}
poly inv(poly a){return inv(a,a.size());}

poly deriv(poly a){
	int n=(int)a.size()-1;
	For(i,0,n-1)a[i]=a[i+1]*(i+1);
	a.resize(n);return a;
}
poly inter(poly a){
	int n=a.size()+1;a.resize(n); initC(n);
	Rep(i,n-1,1)a[i]=a[i-1]*iv[i];
	a[0]=0;return a;
}
poly ln(poly a){
	int n=a.size();
	a=deriv(a)*inv(a),a.resize(n-1);return inter(a);
}
poly exp(poly a,int k){
	int n=1<<k;a.resize(n);
	if(n==1)return one();
	poly f0=exp(a,k-1);f0.resize(n);
	return f0*(one()+a-ln(f0)); 
}
poly exp(poly a){
	int n=a.size();
	a=exp(a,ext(n));a.resize(n);return a;
}
poly div(poly a,poly b){
	int n=a.size(),m=b.size(),k=ext(n-m+1);
	reverse(a.begin(),a.end()),reverse(b.begin(),b.end());
	a.resize(n-m+1),b.resize(n-m+1);
	a=a*inv(b),a.resize(n-m+1),reverse(a.begin(),a.end()); return a;
}
poly modulo(poly a,poly b){
	if(b.size()>a.size())return a;
	int n=b.size()-1;
	a=a-div(a,b)*b;a.resize(n);return a;
}

#define maxn 200005
#define inf 0x3f3f3f3f

signed main()
{
	init(21);
	int n=read()+1,m=read()+1;
	poly f(n),g(m);
	for(auto&x:f)x=read();
	for(auto&x:g)x=read();
	f=f*g;
	for(auto x:f)printf("%d ",x.x);
	return 0;
}

poly sqrt(poly a,int k){
	int n=1<<k;a.resize(n);
	if(n==1)return one();
	poly f0=sqrt(a,k-1);f0.resize(n);
	poly tmp=a*inv(f0);tmp.resize(n);tmp=tmp+f0;
	tmp=tmp*((mod+1)/2);
	return tmp;
}
poly sqrt(poly a){
	int n=a.size();
	a=sqrt(a,ext(n));a.resize(n);return a;
}

poly valF;
vector<poly>solveE(int l,int r){
	if(l==r)return {{valF[l]},{1,(mod-l)%mod}};
	int mid=l+r>>1;
	auto fl=solveE(l,mid),fr=solveE(mid+1,r);
	return {fl[0]*fr[1]+fl[1]*fr[0],fl[1]*fr[1]};
}
poly transE(poly f){
	int n=f.size();valF=f;
	vector<poly>g=solveE(0,n-1);
	poly res=g[0]*inv(g[1]); res.resize(n);
	For(i,0,n-1)res[i]*=ifac[i];
	return res;
}
poly shift(poly f,modint v){
	int n=f.size(); poly g(n); initC(n);
	For(i,0,n-1)f[i]*=fac[i];
	modint pw=1;
	For(i,0,n-1)g[i]=ifac[i]*pw,pw*=v;
	reverse(f.begin(),f.end()),f=f*g,reverse(f.begin(),f.end());
	f.resize(n);
	For(i,0,n-1)f[i]*=ifac[i];
	return f;
}
poly mult(poly a,poly b){
	int n=a.size();
	reverse(a.begin(),a.end());
	a=a*b,a.resize(n);reverse(a.begin(),a.end());return a;
}

```cpp
namespace eva{
	poly A[maxn<<2],f;
	modint x[maxn],y[maxn];
	void dfs1(int p,int l,int r){
		if(l==r)return A[p]={1,-x[l]},void();
		int mid=l+r>>1;
		dfs1(p<<1,l,mid),dfs1(p<<1|1,mid+1,r),A[p]=A[p<<1]*A[p<<1|1];
	}
	void dfs2(int p,int l,int r,poly f){
		if(l==r)return y[l]=f[0],void();
		int mid=l+r>>1; f.resize(r-l+1);
		if(r-l+1<=64){
			dfs2(p<<1,l,mid,mult(f,A[p<<1|1]));
			dfs2(p<<1|1,mid+1,r,mult(f,A[p<<1]));
			return;
		}
		reverse(f.begin(),f.end());
		int k=ext(f.size()+max(A[p<<1].size(),A[p<<1|1].size())); init(k);
		f.resize(1<<k),A[p<<1].resize(1<<k),A[p<<1|1].resize(1<<k);
		ntt(f,k,1),ntt(A[p<<1],k,1),ntt(A[p<<1|1],k,1);
		poly fr(1<<k);
		For(i,0,(1<<k)-1)fr[i]=f[i]*A[p<<1|1][i],f[i]*=A[p<<1][i];
		ntt(f,k,-1),ntt(fr,k,-1);
		f.resize(r-l+1),fr.resize(r-l+1),reverse(f.begin(),f.end()),reverse(fr.begin(),fr.end());
		dfs2(p<<1,l,mid,fr);
		dfs2(p<<1|1,mid+1,r,f);
	}
	void work(poly f,int m){
		dfs1(1,1,m);
		f.resize(max((int)f.size(),m+1));
		A[1].resize(f.size());
		dfs2(1,1,m,mult(f,inv(A[1])));
	}
}