  Adin, Brenti, and Roichman introduced the pairs of statistics $(\ndes,
\nmaj)$ and $(\fdes, \fmaj)$. They showed that these pairs are equidistributed
over the hyperoctahedral group $B_n$, and can be considered "Euler-Mahonian" in
that they generalize the Carlitz identity. Further, they asked whether there
exists a bijective proof of the equidistribution of their statistics. We give
such a bijection, along with a new proof of the generalized Carlitz identity.
