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);
	}
}
{
	ll@m++,@n++,@k[m];
	double@a[n],z[n]{};
	z[0]=m>2?powmod(a[0],sum[i,2,m](k[i]),1009):1;
	ll c=k[0]+(m>1?k[1]*1009:0);
	while(c){
		if(c&1){
			f(n,a,z);
		}
		c>>=1;
		f(n,a,a);
	}
	wt((ll)z(n));
}