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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;
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 int mod=950009857,g=7;
void check(int &x) {
if(x>=mod)x-=mod;
if(x<0)x+=mod;
}
void add(int &x,int v) {
x+=v;
check(x);
}
int Quick_Pow(int a,int b) {
int sum=1;
for(; b; b>>=1,a=1ll*a*a%mod)if(b&1)sum=1ll*sum*a%mod;
return sum;
}
int get_inv(int x) {
return Quick_Pow(x,mod-2);
}
int inv[maxn];
struct NumberTheoreticTransform {
int n,rev[maxn];
int 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]=1ll*omega[i-1]*x%mod;
iomega[i]=get_inv(omega[i]);
}
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));
rev[i]=t;
}
}
void transform(int* a,int* omega) {
for(int i=0; i<n; i++)if(i<rev[i])swap(a[i],a[rev[i]]);
for(int len=2; len<=n; len*=2) {
int mid=len>>1;
for(int* p=a; p!=a+n; p+=len)
for(int i=0; i<mid; i++) {
int t=1ll*omega[n/len*i]*p[mid+i]%mod;
p[mid+i]=p[i]-t,check(p[mid+i]);
add(p[i],t);
}
}
}
void dft(int* a) {
transform(a,omega);
}
void idft(int* a) {
transform(a,iomega);
int x=inv[n];
for(int i=0; i<n; i++)a[i]=1ll*a[i]*x%mod;
}
} ntt;
void polynomial_inverse(const int* a,const int n,int* b) {
if(n==1) {
b[0]=get_inv(a[0]);
return;
}
polynomial_inverse(a,n>>1,b);
int p=n<<1;
static int 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]=1ll*b[i]*((2-1ll*x[i]*b[i]%mod+mod)%mod)%mod;
ntt.idft(b),fill(b+n,b+p,0);
}
void Multiply(const int* a1,const int n1,const int* a2,const int n2,int* ans) {
int n=1;
while(n<n1+n2)n<<=1;
static int c1[maxn],c2[maxn];
copy(a1,a1+n1,c1),fill(c1+n1,c1+n,0);
copy(a2,a2+n2,c2),fill(c2+n2,c2+n,0);
ntt.dft(c1);
ntt.dft(c2);
for(int i=0; i<n; i++)c1[i]=1ll*c1[i]*c2[i]%mod;
ntt.idft(c1);
for(int i=0; i<n1+n2-1; i++)ans[i]=c1[i];
}
void polynomial_lnp(const int* a,int n,int* b) {
static int tmp[maxn];
polynomial_inverse(a,n,tmp);
for(int i=0; i<n-1; i++)b[i]=1ll*a[i+1]*(i+1)%mod;
b[n-1]=0;
Multiply(b,n,tmp,n,b);
fill(b+n,b+(n<<1),0),fill(tmp,tmp+n,0);
for(int i=n-1; i>=1; i--)b[i]=1ll*b[i-1]*inv[i]%mod;
b[0]=0;
}
void polynomial_exp(const int *a,int n,int* b) {
if(n==1) {
b[0]=1;
return;
}
polynomial_exp(a,n>>1,b);
int p=n<<1;
static int x[maxn];
polynomial_lnp(b,n,x);
for(int i=0; i<n; i++)x[i]=-x[i]+a[i],check(x[i]);
add(x[0],1);
Multiply(b,n,x,n,b),fill(b+n,b+p,0);
}
int n,m;
int G[maxn],inv_G[maxn],ln_inv_G[maxn],inv_G_n[maxn];
int main() {
n=Get_Int();
m=Get_Int();
G[0]=1;
for(int i=1; i<=m; i++)G[Get_Int()-1]=mod-1;
int p=1;
while(p<n)p<<=1;
inv[1]=1;
for(int i=2; i<=(p<<1); i++)inv[i]=1ll*(mod-mod/i)*inv[mod%i]%mod;
ntt.init(p<<1);
polynomial_inverse(G,p,inv_G);
fill(inv_G+n,inv_G+p,0);
polynomial_lnp(inv_G,p,ln_inv_G);
fill(ln_inv_G+n,ln_inv_G+p,0);
for(int i=0; i<p; i++)ln_inv_G[i]=1ll*ln_inv_G[i]*n%mod;
polynomial_exp(ln_inv_G,p,inv_G_n);
printf("%d\n",1ll*inv_G_n[n-1]*inv[n]%mod);
return 0;
}
|
