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];
	double z[n]{1};
	ll a0=a[0];
	ll a1=n>1?a[1]:0;
	ll aa=a[0];
	if(true){
		ll c=k[0];
		while(c){
			if(c&1){
				f(n,a,z);
			}
			c>>=1;
			f(n,a,a);
		}
	}
	ll e=1;
	if(m>1&&n>1009){
		e=2;
		ll c=k[1];
		while(c){
			if(c&1){
				rep(i,1009,n){
					z[i]=fmod(z[i]*a0+z[i-1009]*a1,1009);
				}
				rep(i,1009){
					z[i]=fmod(z[i]*a0,1009);
				}
			}
			c>>=1;
			(a0,a1)=(a0*a0%1009,a0*a1*2%1009);
		}
	}
	ll b=m>e?powmod(aa,sum[i,e,m](k[i]),1009):1;
	wt((ll)z(n)*b%1009);
}