Are there any papers on the cohomology of the classifying space of the general linear supergroup $GL(n, m)$ or unitary supergroup $U(n, m)$?

I know basically nothing about supergeometry. It seems that in my situation I just need to know the cohomology of the classifying spaces of the supergroups mentioned above. When I google for this topic, I basically found nothing, but other information seems to imply that ordinary cohomology theory (for example, singular or de Rham) cannot detect the superdifferentiable structure of supermanifolds, so some cohomology theories for supermanifolds were invented (I know there are different classes of supermanifolds, but I don't the groups or its classifying spaces belong to which class). Thus, as a start, I think I need to know the ordinary cohomology of $BGL(n, m)$ and $BU(n, m)$ (if it exists).

Thanks.