  We show that any symplectically aspherical/Calabi-Yau filling of
$Y:=\partial(V\times \mathbb{D})$ has vanishing symplectic cohomology for any
Liouville domain $V$. In particular, we make no topological requirement on the
filling and $c_1(V)$ can be nonzero. Moreover, we show that for any
symplectically aspherical/Calabi-Yau filling $W$ of $Y$, the interior
$\mathring{W}$ is diffeomorphic to the interior of $V\times \mathbb{D}$ if
$\pi_1(Y)$ is abelian and $\dim V\ge 4$. And $W$ is diffeomorphic to $V\times
\mathbb{D}$ if moreover the Whitehead group of $\pi_1(Y)$ is trivial.
