k-path problem - P, NP or NPC? I need to determine which complexity class this problem belongs to:


  Given a graph $G(V, E)$, two vertices $u$ and $v$ and a natural number $k$, does a path of length $k$ exist between thesee two vertices?


How can I approach this problem to solve it?
If the path has to be simple reduce the HamiltonPath problem to this to show that's NP-complete, otherwise (not necessarily simple paths) take the $k$-th power of the adjacency matrix, whose entry corresponding to $u$ and $v$ not only contains whether there is such a path, but also the number of such paths.