void f(ll n,double*a,double*r){
	convolution(a,n,r,n,r,n);
	rep(i,n){
		r[i]=fmod(floor(r[i]+.5),1009);
	}
}
void g(ll n,double*r){
	convolution(r,n,r,n);
	rep(i,n){
		r[i]=fmod(floor(r[i]+.5),1009);
	}
}
{
	ll@m++,@n++,@k[m];
	double@a[n];
	double z[n]{1};
	ll b=a[0];
	ll c=k[0];
	while(c){
		if(c&1){
			f(n,a,z);
		}
		c>>=1;
		g(n,a);
	}
	b=powmod(b,sum[i,1,m](k[i]),1009);
	wt((ll)z(n)*b%1009);
}