Lattice structure realization of an all-pole system Given an IIR system with the system function,

$$ H(z) = \frac{1}{2 + 1.4z^{-1} + 1.8z^{-2}} $$

I need to draw the lattice structure realization.

I have drawn the lattice structure for $\frac{1}{1 + 0.7z^{-1} + 0.9z^{-2}}$, which is shown in the figure below. 



Now since $H(z) = \frac{1}{2(1 + 0.7z^{-1} + 0.9z^{-2})} $, should I multiply the signal $x(n)$ by $2$ or $1/2$ before feeding to the system? My intuition is that I should multiply with $\frac 1 2$, but then since $2$ appears as the multiple in the denominator polynomial, I got confused.
Rearrange into a difference equation form and your answer will become clearer!