Cylinders over affine surfaces

For an affine variety $S$ we consider the ring $AK(S),$ which is the intersection of the rings of constants of all locally-nilpotent derivations of the ring $\Cal {O}(S).$ We show that $AK(S\times\Bbb {C}^n)=AK(S)$ for a smooth affine surface $S$ with $H^2(S,\Bbb {Z})=\{0\}.$