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| #include<algorithm>
#include<iostream>
#include<iomanip>
#include<cstring>
#include<cstdlib>
#include<climits>
#include<vector>
#include<cstdio>
#include<cmath>
#include<queue>
using namespace std;
typedef long long LL;
inline const int Get_Int() {
int num=0,bj=1;
char x=getchar();
while(x<'0'||x>'9') {
if(x=='-')bj=-1;
x=getchar();
}
while(x>='0'&&x<='9') {
num=num*10+x-'0';
x=getchar();
}
return num*bj;
}
const int maxn=262144+5;
const LL mod=1004535809,g=3;
LL Quick_Pow(LL a,LL b) {
LL sum=1;
for(; b; b>>=1,a=a*a%mod)if(b&1)sum=sum*a%mod;
return sum;
}
LL inv(LL x) {
return Quick_Pow(x,mod-2);
}
struct NumberTheoreticTransform {
int n;
LL omega[maxn],iomega[maxn];
void init(int n) {
this->n=n;
int x=Quick_Pow(g,(mod-1)/n);
omega[0]=iomega[0]=1;
for(int i=1; i<n; i++) {
omega[i]=omega[i-1]*x%mod;
iomega[i]=inv(omega[i]);
}
}
void transform(LL* a,LL* omega) {
int k=log2(n);
for(int i=0; i<n; i++) {
int t=0;
for(int j=0; j<k; j++)if(i&(1<<j))t|=(1<<(k-j-1));
if(i<t)swap(a[i],a[t]);
}
for(int len=2; len<=n; len*=2) {
int mid=len>>1;
for(LL* p=a; p!=a+n; p+=len)
for(int i=0; i<mid; i++) {
LL t=omega[n/len*i]*p[mid+i]%mod;
p[mid+i]=(p[i]-t+mod)%mod;
p[i]=(p[i]+t)%mod;
}
}
}
void dft(LL* a) {
transform(a,omega);
}
void idft(LL* a) {
transform(a,iomega);
LL x=inv(n);
for(int i=0; i<n; i++)a[i]=a[i]*x%mod;
}
} ntt;
void polynomial_inverse(const LL* a,const int n,LL* b) {
if(n==1) {
b[0]=inv(a[0]);
return;
}
polynomial_inverse(a,n>>1,b);
int p=n<<1;
static LL x[maxn];
copy(a,a+n,x),fill(x+n,x+p,0);
ntt.init(p),ntt.dft(x),ntt.dft(b);
for(int i=0; i<p; i++)b[i]=b[i]*((2-x[i]*b[i]%mod+mod)%mod)%mod;
ntt.idft(b),fill(b+n,b+p,0);
}
LL n,fac[maxn],invi[maxn],invf[maxn],g1[maxn],G[maxn],C[maxn],_G[maxn];
int main() {
n=Get_Int();
fac[0]=invf[0]=invi[1]=1;
for(int i=1; i<=n; i++) {
fac[i]=fac[i-1]*i%mod;
if(i!=1)invi[i]=(mod-mod/i)*invi[mod%i]%mod;
invf[i]=invf[i-1]*invi[i]%mod;
}
g1[0]=g1[1]=1;
for(int i=2; i<=n; i++)g1[i]=Quick_Pow(2,(LL)i*(i-1)/2%(mod-1));
for(int i=0; i<=n; i++)G[i]=g1[i]*invf[i]%mod;
for(int i=1; i<=n; i++)C[i]=g1[i]*invf[i-1]%mod;
int p=1;
while(p<n+1)p<<=1;
polynomial_inverse(G,p,_G);
fill(_G+n+1,_G+p,0);
p<<=1;
ntt.init(p);
ntt.dft(_G);
ntt.dft(C);
for(int i=0; i<=p; i++)_G[i]=_G[i]*C[i]%mod;
ntt.idft(_G);
printf("%lld\n",_G[n]*fac[n-1]%mod);
return 0;
}
|
