NP-completeness of the exact distance problem I am currently learning about NP-complete problems and I want to make sure my understanding is correct.

Here is a problem I am working on currently:


  The exact distance problem is, given an edge-weighted graph $G = (V,E)$, vertices $v_1,v_k$, and a distance $D$, is there a simple path from $v_1$ to $v_k$ with length exactly $D$?


The first part of my solution is proving that the problem is in NP. I did this by picking a solution to the problem and proving that we can verify the solution in polynomial time. My proof showed that we can verify the solution in $O(mn)$ time, where $m$ is the number of edges and $n$ is the number of vertices. 

The next part is showing that a problem we know to be NP-complete can be reduced to the exact distance problem. I am having trouble deciding on an easy NP-Complete problem to use in this part. Would the Hamiltonian Path problem be a good choice?
Yes. ​ Keep in mind exactly what the inputs to each problem are.