On the divisor class group of double solids

For a double solid $V \to \mathbb P^3$ branched over a surface $B$ with only ordinary double points as singularities we give a set of generators of divisor class group $Pic(V)=\cong H^2(V,\mathbb Z)$ in terms of contact surfaces of $B$. As an application we give a condition when $H^*(V,\mathbb Z)$ has no 2-torsion.