ac.commutative algebra - Support sets along a ring homomorphism.

Let $(R,m)$ and $(S,n)$ be commutative noetherian local rings, and $f: Rrightarrow S$ be a local homomorphism (i.e., $f(m) subseteq n$) with $S$ flat as $R$-module. If $M$ is a finite generated $R$-module, then what is the relation between $Supp_s(Motimes S)$ and $Supp_R(M)$? Thanks in advance!