Compression with wildcards: All k-models of a binary decision diagram

Given a Binary Decision Diagram $B$ of a Boolean function $\varphi$ in $n$ variables, it is well known that all $\varphi$-models can be enumerated in output polynomial time, and in a compressed way (using don't-care symbols). We show that all $N$ many $\varphi$-models of fixed Hamming-weight $k$ can be enumerated as well in time polynomial in $n$ and $|B|$ and $N$. Furthermore, using novel wildcards, again enables a compressed enumeration of these models.