  Recently, Mansour and Shattuck related the total number of humps in all of
the $(k, a)$-paths of order $n$ to the number of super $(k, a)$-paths, which
generalized previous results concerning the cases when $k = 1$ and $a = 1$ or
$a = \infty$. They also derived a relation on the total number of peaks in all
of the $(k, a)$-paths of order $n$ and the number of super $(k, a)$-paths, and
asked for bijective proofs. In this paper, we will give bijective proofs of
these two relations.
