分析
https://www.luogu.org/blog/DRA/solution-p4841
代码(似乎附赠了一个全家桶呢)
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("-falign-jumps")
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-funroll-loops")
#pragma GCC optimize("-fwhole-program")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("inline-functions")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-fstrict-overflow")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-fcse-skip-blocks")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("inline-small-functions")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("-funsafe-loop-optimizations")
#pragma GCC optimize("inline-functions-called-once")
#pragma GCC optimize("-fdelete-null-pointer-checks")
#include<bits/stdc++.h>
using namespace std;
#define int long long
const int g = 3;
const int mod = 1004535809;
int G,a[400100],b[400100],c[400100],len,r[400100],a1[400100],b1[400100],ib[400100],ans[400100],ans2[400100];
inline int pw(int x,int p){
int res=1;
while(p){if(p&1)res=res*x%mod;x=x*x%mod,p>>=1;}
return res;
}
#define pi acos(-1.0)
struct node {
double x,y;
};
node A[2000100],B[2000100];
inline node operator + (const node x,const node y){return (node){x.x+y.x,x.y+y.y};}
inline node operator - (const node x,const node y){return (node){x.x-y.x,x.y-y.y};}
inline node operator * (const node x,const node y){return (node){x.x*y.x-x.y*y.y,x.x*y.y+x.y*y.x};}
inline void fft(node a[],int f,int n){
int i,j,k;
for(i=0;i<n;i++)if(i<r[i])swap(a[i],a[r[i]]);
for(i=1;i<n;i<<=1){
node wn=(node){cos(pi/i),f*sin(pi/i)};
for(j=0;j<n;j+=(i<<1)){
node w=(node){1,0},p,q;
for(k=0;k<i;k++,w=w*wn){
p=a[j+k],q=a[i+j+k]*w;
a[j+k]=p+q,a[i+j+k]=p-q;
}
}
}
if(f==-1)for(i=0;i<n;i++)a[i].x=a[i].x/n;
return;
}
inline void get_fft_mul(node A[],node B[],int n){
int N=1;
for(N=1;N<=n;N<<=1)len++;
for(int i=0;i<N;i++)r[i]=((r[i>>1]>>1)|((i&1)<<(len-1)));
fft(A,1,N),fft(B,1,N);
for(int i=0;i<N;i++)A[i]=A[i]*B[i];
fft(A,-1,N);
for(int i=0;i<N;i++)ans[i]=(int)(A[i].x+0.5);
return;
}
inline void fwt_or(int a[],int f,int n){
int i,j,k;
for(i=1;i<n;i<<=1)
for(j=0;j<n;j+=(i<<1))
for(k=0;k<i;k++){
if(f==1)a[i+j+k]=(a[j+k]+a[i+j+k])%mod;
else a[i+j+k]=(a[i+j+k]+mod-a[j+k])%mod;
}
}
inline void fwt_and(int a[],int f,int n){
int i,j,k;
for(i=1;i<n;i<<=1)
for(j=0;j<n;j+=(i<<1))
for(k=0;k<i;k++){
if(f==1)a[j+k]=(a[j+k]+a[i+j+k])%mod;
else a[j+k]=(a[j+k]+mod-a[i+j+k])%mod;
}
}
inline void fwt_xor(int a[],int f,int n){
int i,j,k,inv2=pw(2,mod-2);
for(i=1;i<n;i<<=1)
for(j=0;j<n;j+=(i<<1))
for(k=0;k<i;k++){
int x=a[j+k],y=a[i+j+k];
a[j+k]=(x+y)%mod;a[i+j+k]=(x+mod-y)%mod;
}
if(f==-1)for(i=0;i<n;i++)a[i]=a[i]*inv2%mod;
}
inline void ntt(int a[],int opt,int n){
int i,j,k,inv=pw(n,mod-2),now,wn,w,p,q;
for(i=0;i<n;i++)if(i<r[i])swap(a[i],a[r[i]]);
for(i=1;i<n;i<<=1){
now=(opt==1?g:G),wn=pw(now,(mod-1)/(i<<1));
for(j=0;j<n;j+=(i<<1))
for(k=0,w=1;k<i;k++,w=w*wn%mod)
p=a[j+k],q=a[i+j+k]*w%mod,a[j+k]=(p+q)%mod,a[i+j+k]=(p-q+mod)%mod;
}
if(opt==-1)for(i=0;i<n;i++)a[i]=a[i]*inv%mod;
return;
}
inline void cdq_fft(int le,int ri){
if(le==ri){
//.....
return;
}
int i,j,k,n,m=ri-le,mid=(le+ri)>>1;len=0;
cdq_fft(le,mid);
for(n=1;n<=2*(m+1);n<<=1)len++;
for(i=0;i<n;i++)a1[i]=b1[i]=0;
for(i=0;i<n;i++)r[i]=((r[i>>1]>>1)|((i&1)<<(len-1)));
//for(i=0;i<=mid-le;i++)b1[i]=b[i+le];
//for(i=0;i<=m;i++)a1[i]=a[i];
ntt(a1,1,n),ntt(b1,1,n);
//for(i=0;i<n;i++)b1[i]=a1[i]*b1[i]%mod;
ntt(b1,-1,n);
for(i=mid+1;i<=ri;i++)b[i]=(b[i]+b1[i-le])%mod;
cdq_fft(mid+1,ri);
return;
}
inline void get_inv(int x,int a[],int b[]){
if(x==1){b[0]=pw(a[0],mod-2);return;}
int i,j,k,n;get_inv((x+1)>>1,a,b);len=0;
for(n=1;n<(x<<1);n<<=1)len++;
for(i=0;i<n;i++)r[i]=((r[i>>1]>>1)|((i&1)<<(len-1)));
for(i=0;i<x;i++)c[i]=a[i];for(i=x;i<n;i++)c[i]=0;
ntt(b,1,n),ntt(c,1,n);
for(i=0;i<n;i++)b[i]=(2-c[i]*b[i]%mod+mod)%mod*b[i]%mod;
ntt(b,-1,n);for(i=x;i<n;i++)b[i]=0;return;
}
inline void get_dao(int n,int a[],int b[]){
for(int i=0;i<n;i++)b[i]=a[i+1]*(i+1)%mod;
b[n-1]=0;return;
}
inline void get_ji(int n,int a[],int b[]){
for(int i=n-1;i>0;i--)b[i]=a[i-1]*pw(i,mod-2)%mod;
b[0]=0;return;
}
inline void get_mul(int n,int a[],int b[]){
int i,j,k;
ntt(a,1,n),ntt(b,1,n);
for(i=0;i<n;i++)a[i]=a[i]*b[i]%mod;
ntt(a,-1,n);return;
}
inline void get_ln(int n,int a[],int b[]){
for(int i=0;i<(n<<1);i++)b[i]=0;
get_inv(n,a,b);
int N;len=0;
for(N=1;N<(n<<1);N<<=1)len++;
for(int i=0;i<N;i++)r[i]=((r[i>>1]>>1)|((i&1)<<(len-1)));
get_dao(N,a,a1);
get_mul(N,a1,b);
get_ji(N,a1,b);
for(int i=0;i<N;i++)a1[i]=0;
return;
}
inline void get_exp(int n,int a[],int b[]){
if(n==1){b[0]=1;return;}
get_exp((n+1)>>1,a,b);
get_ln(n,b,b1);
b1[0]=(a[0]+1-b1[0]+mod)%mod;
for(int i=1;i<n;i++)b1[i]=(a[i]-b1[i]+mod)%mod;
int N;len=0;
for(N=1;N<(n<<1);N<<=1)len++;
for(int i=0;i<N;i++)r[i]=((r[i>>1]>>1)|((i&1)<<(len-1)));
for(int i=n;i<N;i++)b[i]=b1[i]=0;
ntt(b,1,N),ntt(b1,1,N);
for(int i=0;i<N;i++)b[i]=b[i]*b1[i]%mod;
ntt(b,-1,N);
for(int i=n;i<N;i++)b[i]=b1[i]=0;
}
inline int read_pw(){
int x=0;char s=getchar();
while(!isdigit(s))s=getchar();
while(isdigit(s))x=((x<<3)+(x<<1)+(s-'0'))%mod,s=getchar();
return x;
}
inline void get_pw(int n,int a[],int b[],int k){
get_ln(n,a,b);
for(int i=0;i<n;i++)b[i]=b[i]*k%mod;
get_exp(n,b,ans);
return;
}
inline void get_div(int n,int m,int a1[],int b1[]){
int i,j,k;
for(i=0;i<n;i++)a[i]=a1[n-1-i];
for(i=0;i<m;i++)b[i]=b1[m-1-i],ib[i]=0;
for(i=n-m+2;i<m;i++)b[i]=0;
get_inv(n-m+1,b,ib);
int N;len=0;
for(N=1;N<(n<<1);N<<=1)len++;
for(int i=0;i<N;i++)r[i]=((r[i>>1]>>1)|((i&1)<<(len-1)));
get_mul(N,a,ib);
int _n=n-m+1;
for(i=0;i<_n;i++)ans[i]=a[_n-1-i],printf("%lld ",ans[i]);
for(i=0;i<m;i++)b[i]=b1[m-1-i];
for(i=m;i<N;i++)b[i]=0;
puts("");
get_mul(N,ans,b1);
for(i=0;i<m-1;i++)ans2[i]=(a1[i]-ans[i]+mod)%mod,printf("%lld ",ans2[i]);
puts("");
return;
}
int fac[100100],inv[100100];
signed main(){
G=pw(g,mod-2);
int n,m,i,k;
scanf("%lld",&n);
//k=read_pw();
k=1;
fac[0]=1;
for(i=1;i<=n;i++)fac[i]=fac[i-1]*i%mod;
inv[n]=pw(fac[n],mod-2);
for(i=n-1;i>=0;i--)inv[i]=inv[i+1]*(i+1)%mod;
for(i=0;i<=n;i++)a[i]=pw(2,i*(i-1)/2)*inv[i]%mod;
get_inv(n+1,a,b);
int N;len=0;
for(N=1;N<=n+1;N<<=1)len++;
for(i=0;i<N;i++)r[i]=((r[i>>1]>>1)|((i&1)<<(len-1)));
for(i=0;i<N;i++)a[i]=0;
for(i=1;i<=n;i++)a[i]=pw(2,i*(i-1)/2)*inv[i-1]%mod;
get_mul(N,a,b);a[0]=1;
for(i=1;i<N;i++)a[i]=a[i]*fac[i-1]%mod*inv[i]%mod;
for(i=N;i<=100000;i++)a[i]=0;
memset(b,0,sizeof(b));
get_pw(n+1,a,b,k);
printf("%lld\n",ans[n]*fac[n]%mod);
return 0;
}