【LOJ556】咱們去燒菜吧（多項式exp）

傳送門

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和這道題是一樣的，就不寫題解了：付公主的揹包

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代碼：

#include<bits/stdc++.h>
#define ll long long
#define re register
#define cs const

namespace IO{
	inline char gc(){
		static cs int Rlen=1<<22|1;static char buf[Rlen],*p1,*p2;
		return (p1==p2)&&(p2=(p1=buf)+fread(buf,1,Rlen,stdin),p1==p2)?EOF:*p1++;
	}template<typename T>T get_integer(){
		char c;bool f=false;while(!isdigit(c=gc()))f=c=='-';T x=c^48;
		while(isdigit(c=gc()))x=((x+(x<<2))<<1)+(c^48);return f?-x:x;
	}inline int gi(){return get_integer<int>();}
}using namespace IO;

using std::cerr;
using std::cout;

cs int mod=998244353;
inline int add(int a,int b){return a+b>=mod?a+b-mod:a+b;}
inline int dec(int a,int b){return a-b<0?a-b+mod:a-b;}
inline int mul(int a,int b){ll r=(ll)a*b;return r>=mod?r%mod:r;}
inline void Inc(int &a,int b){a+=b-mod;a+=a>>31&mod;}
inline void Dec(int &a,int b){a-=b;a+=a>>31&mod;}
inline void Mul(int &a,int b){a=mul(a,b);}
inline int po(int a,int b){int r=1;for(;b;b>>=1,Mul(a,a))if(b&1)Mul(r,a);return r;}
inline void ex_gcd(int a,int b,int &x,int &y){
	if(!b){x=1,y=0;return;}ex_gcd(b,a%b,y,x);y-=a/b*x;
}inline int Inv(int a){int x,y;ex_gcd(mod,a,y,x);return x+(x>>31&mod);}

cs int bit=18,SIZE=1<<bit|7;

int r[SIZE],*w[bit+1],Log[SIZE],inv[SIZE],len,inv_len;
void init_omega(){
	for(int re i=1;i<=bit;++i)w[i]=new int[1<<(i-1)];
	int wn=po(3,(mod-1)>>bit);w[bit][0]=1;
	for(int re i=1;i<(1<<(bit-1));++i)
		w[bit][i]=mul(w[bit][i-1],wn);
	for(int re i=bit-1;i;--i)
		for(int re j=0;j<(1<<(i-1));++j)
			w[i][j]=w[i+1][j<<1];
	inv[1]=1;for(int re i=2;i<SIZE;++i)
		inv[i]=mul(mod-mod/i,inv[mod%i]);
	for(int re i=2;i<SIZE;++i)
		Log[i]=Log[i-1]+((1<<Log[i-1])<i);
}
void DFT(int *A){
	for(int re i=1;i<len;++i)
		if(i<r[i])std::swap(A[i],A[r[i]]);
	for(int re i=1,d=1;i<len;i<<=1,++d)
		for(int re j=0;j<len;j+=i<<1)
			if(i<8){
				for(int re k=0;k<i;++k){
					int &t1=A[j+k],&t2=A[j+k+i];
					int t=mul(t2,w[d][k]);
					t2=dec(t1,t);Inc(t1,t); 
				}
			}else {
#define work(p)	\
{	\
	int &t1=A[j+k+p],&t2=A[j+k+i+p];	\
	int t=mul(t2,w[d][k+p]);			\
	t2=dec(t1,t);Inc(t1,t);				\
}
				for(int re k=0;k<i;k+=8){
					work(0);work(1);work(2);work(3);
					work(4);work(5);work(6);work(7);
				}
#undef work
			}
}void IDFT(int *A){
	DFT(A);std::reverse(A+1,A+len);
	for(int re i=0;i<len;++i)Mul(A[i],inv_len);
}void init_len(int l){
	len=l;inv_len=inv[l];
	for(int re i=1;i<len;++i)r[i]=r[i>>1]>>1|((i&1)?l>>1:0);
}

using Poly=std::vector<int>;
inline void DFT(Poly &A){DFT(&A[0]);}
inline void IDFT(Poly &A){IDFT(&A[0]);}

int A[SIZE],B[SIZE];
Poly operator*(cs Poly &a,cs Poly &b){
	if(!a.size()||!b.size())return Poly(0);
	int deg=a.size()+b.size()-1;init_len(1<<Log[deg]);
	memcpy(A,&a[0],a.size()<<2);
	memset(A+a.size(),0,(len-a.size())<<2);
	memcpy(B,&b[0],b.size()<<2);
	memset(B+b.size(),0,(len-b.size())<<2);
	DFT(A);DFT(B);for(int re i=0;i<len;++i)Mul(A[i],B[i]);
	IDFT(A);return Poly(A,A+deg);
}

Poly Inv(cs Poly &a,int lim){
	int n=a.size();Poly c,b(1,Inv(a[0]));
	for(int re l=4;(l>>2)<lim;l<<=1){
		init_len(l);c.resize(l>>1);
		for(int re i=0;i<(l>>1);++i)
			c[i]=i<n?a[i]:0;
		c.resize(l);DFT(c);
		b.resize(l);DFT(b);
		for(int re i=0;i<l;++i)
			Mul(b[i],dec(2,mul(b[i],c[i])));
		IDFT(b);b.resize(l>>1);
	}b.resize(lim);return b;
}

Poly Deriv(Poly a){
	if(!a.size())return Poly(0);
	for(int re i=0;i+1<(int)a.size();++i)
		a[i]=mul(a[i+1],i+1);
	a.pop_back();return a;
}

Poly Integ(Poly a){
	if(!a.size())return Poly(0);
	a.push_back(0);
	for(int re i=a.size()-1;i;--i)
		a[i]=mul(a[i-1],inv[i]);
	a[0]=0;return a;
}

Poly Ln(cs Poly &a,int lim){
	Poly b=Deriv(a)*Inv(a,lim);
	b.resize(lim+1);return Integ(b);
}

Poly Exp(cs Poly &a,int lim){
	int n=a.size();Poly c,b(1,1);
	for(int re i=2;(i>>1)<lim;i<<=1){
		c=Ln(b,i);Dec(c[0],1);
		for(int re j=0;j<i;++j)
			c[j]=dec(j<n?a[j]:0,c[j]);
		b=b*c;b.resize(i);
	}b.resize(lim);return b;
}

cs int N=1e5+7;
int n,m,ct[N];
Poly F;
 
void Main(){
	n=gi(),m=gi();init_omega();
	F.resize(n+1);while(m--){
		int a=gi(),b=gi();
		if(a<=n)Inc(ct[a],1);
		if(b&&(b+1ll)*a<=n)Dec(ct[a*(b+1)],1);
	}for(int re i=1;i<=n;++i)if(ct[i])
		for(int re j=1,t=i;t<=n;t+=i,++j)
			Inc(F[t],mul(ct[i],inv[j]));
	F=Exp(F,n+1);
	for(int re i=1;i<=n;++i)cout<<F[i]<<"\n";
}

void file(){
#ifdef zxyoi
	freopen("knapsack.in","r",stdin);
#endif
}
signed main(){file();Main();return 0;}