【LOJ #2271】「SDOI2017」遗忘的集合（多项式Ln+任意模数NTT）

传送门

简单推到可以得到
设$a_i=[iin S]$
那么
$Ln(f)=sum_{i}a_isum_{j=1}^{infty}frac{x^{ij}}{j}$
$=sum_{T}x^{T}sum_{d|T}frac{d}{T}a_d$
$=sum_{T}x^TTsum_{d|T}a_dd$
于是对于从小到大枚举每个数枚举倍数更新即可

由于极其恶心的任意模数，要写$MTT$

#include<bits/stdc++.h>
using namespace std;
#define cs const
#define pb push_back
#define pii pair<int,int>
#define fi first
#define se second
#define ll long long
#define re register
cs int RLEN=1<<20|1;
inline char gc(){
	static char ibuf[RLEN],*ib,*ob;
	(ib==ob)&&(ob=(ib=ibuf)+fread(ibuf,1,RLEN,stdin));
	return (ib==ob)?EOF:*ib++;
}
inline int read(){
	char ch=gc();
	int res=0;bool f=1;
	while(!isdigit(ch))f^=ch=='-',ch=gc();
	while(isdigit(ch))res=(res+(res<<2)<<1)+(ch^48),ch=gc();
	return f?res:-res;
}
int mod;
inline int add(int a,int b){return (a+=b)>=mod?(a-mod):a;}
inline int dec(int a,int b){a-=b;return a+(a>>31&mod);}
inline int mul(int a,int b){static ll r;r=1ll*a*b;return (r>=mod)?(r%mod):r;}
inline void Add(int &a,int b){a+=b;(a>=mod)?(a-=mod):0;}
inline void Dec(int &a,int b){a-=b,a+=a>>31&mod;}
inline void Mul(int &a,int b){static ll r;r=1ll*a*b;a=(r>=mod)?(r%mod):r;}
inline int ksm(int a,int b,int res=1){for(;b;b>>=1,Mul(a,a))(b&1)&&(Mul(res,a),1);return res;}
inline int Inv(int x){return ksm(x,mod-2);}
struct plx{
	double x,y;
	plx(double _x=0,double _y=0):x(_x),y(_y){}
	friend inline plx operator +(cs plx &a,cs plx &b){
		return plx(a.x+b.x,a.y+b.y);
	}
	friend inline plx operator -(cs plx &a,cs plx &b){
		return plx(a.x-b.x,a.y-b.y);
	}
	friend inline plx operator *(cs plx &a,cs plx &b){
		return plx(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x);
	}
	inline plx conj()cs{return plx(x,-y);}
};
#define poly vector<int>
cs int C=21,M=(1<<15)-1;
cs double pi=acos(-1);
vector<plx> w[C+1];
int rev[(1<<C)|5],inv[(1<<C)|5];
inline void init_rev(int lim){
	for(int i=0;i<lim;i++)rev[i]=(rev[i>>1]>>1)|((i&1)*(lim>>1));
}
inline void init_w(){
	for(int i=1;i<=C;i++)w[i].resize(1<<(i-1));
	plx wn=plx(cos(pi/(1<<(C-1))),sin(pi/(1<<(C-1))));
	w[C][0]=plx(1,0);
	inv[0]=inv[1]=1;
	for(int i=2;i<(1<<(C-1));i++)inv[i]=mul(mod-mod/i,inv[mod%i]);
	for(int i=1;i<(1<<(C-1));i++){
		if(i&31)w[C][i]=w[C][i-1]*wn;
		else w[C][i]=plx(cos(pi*i/(1<<(C-1))),sin(pi*i/(1<<(C-1))));
	}
	for(int i=C-1;i;i--)
	for(int j=0;j<(1<<(i-1));j++)w[i][j]=w[i+1][j<<1];
}
inline void fft(plx *f,int lim,int kd){
	for(int i=0;i<lim;i++)if(i>rev[i])swap(f[i],f[rev[i]]);
	plx a0,a1;
	for(int mid=1,l=1;mid<lim;mid<<=1,l++)
	for(int i=0;i<lim;i+=(mid<<1))
	for(int j=0;j<mid;j++)
	a0=f[i+j],a1=f[i+j+mid]*w[l][j],f[i+j]=a0+a1,f[i+j+mid]=a0-a1;
	if(kd==-1){
		reverse(f+1,f+lim);
		for(int i=0;i<lim;i++)f[i].x/=lim,f[i].y/=lim;
	}
}
inline poly operator *(poly A,poly B){
	static plx a[(1<<C)|5],b[(1<<C)|5],c[(1<<C)|5],d[(1<<C)|5],da,db,dc,dd;
	int deg=A.size()+B.size()-1,lim=1;
	while(lim<deg)lim<<=1;
	A.resize(lim),B.resize(lim);
	for(int i=0;i<lim;i++)a[i]=plx(A[i]&M,A[i]>>15),b[i]=plx(B[i]&M,B[i]>>15);
	init_rev(lim);
	fft(a,lim,1),fft(b,lim,1);
	for(int i=0;i<lim;i++){
		int j=(lim-i)&(lim-1);
		da=(a[i]+a[j].conj())*plx(0.5,0);
		db=(a[j].conj()-a[i])*plx(0,0.5);
		dc=(b[i]+b[j].conj())*plx(0.5,0);
		dd=(b[j].conj()-b[i])*plx(0,0.5);
		c[i]=(da*dc)+((da*dd)*plx(0,1));
		d[i]=(db*dd)+((db*dc)*plx(0,1));
	}
	fft(c,lim,-1),fft(d,lim,-1);
	poly ret(lim);
	for(int i=0;i<lim;i++){
		ll da=(ll)(d[i].x+0.5)%mod,db=(ll)(d[i].y+0.5)%mod,dc=(ll)(c[i].y+0.5)%mod,dd=(ll)(c[i].x+0.5)%mod;
		ret[i]=((da<<30)+((db+dc)<<15)+dd)%mod;
	}
	return ret;
}
inline poly Inv(poly a,int deg){
	poly b(1,Inv(a[0])),c;
	for(int lim=4;lim<(deg<<2);lim<<=1){
		init_rev(lim);
		c=a,c.resize(lim>>1);
		b.resize(lim),c.resize(lim);
		c=c*b*b;
		for(int i=0;i<(lim>>1);i++)
		b[i]=dec(mul(2,b[i]),c[i]);
		b.resize(lim>>1);
	}
	b.resize(deg);return b;
}
inline poly deriv(poly a){
	for(int i=0;i+1<a.size();i++)a[i]=mul(a[i+1],i+1);
	a.pop_back();return a;
}
inline poly integ(poly a){
	a.pb(0);
	for(int i=(int)a.size()-1;i;i--)a[i]=mul(a[i-1],inv[i]);
	a[0]=0;return a;
}
inline poly Ln(poly a,int deg){
	a=integ(Inv(a,deg)*deriv(a)),a.resize(deg);return a;
}
cs int N=(1<<19)|5;
int n,ans[N];
poly f;
int main(){
	#ifdef Stargazer
	freopen("lx.cpp","r",stdin);
	#endif
	n=read(),mod=read();
	init_w();
	f.resize(n+1),f[0]=1;
	for(int i=1;i<=n;i++)f[i]=read();
	f=Ln(f,n+1);
	for(int i=1;i<=n;i++)Mul(f[i],i);
	for(int i=1;i<=n;i++){
		for(int j=i+i;j<=n;j+=i)
		Dec(f[j],f[i]);
	}
	int cnt=0;
	for(int i=1;i<=n;i++)if(f[i])cnt++;
	cout<<cnt<<'
';
	for(int i=1;i<=n;i++)if(f[i])cout<<i<<" ";
}