  We introduce a new class of superconductors (SCs) in two spatial dimensions
with time reversal symmetry and reflection (i.e., mirror) symmetry. In the
absence of interactions, topological classes of these SCs are distinguished by
an integer-valued ($\mathbb{Z}$) topological invariant. When interactions are
included, we show that the topological classification is modified to
$\mathbb{Z}_8$. This clearly demonstrates that interactions can have
qualitative effect on topological classifications of gapped states of matter in
more than one dimension.
