Consider the following two problems:
A. Given a directed graph and a parameter $k$, determine if it contains a path (not necessarily simple) of length $k$.
B. Given a directed graph, two vertices $s,t$ and a parameter $k$, determine if the graph contains a path from $s$ to $t$ (not necessarily simple) of length $k$.
How can I reduce problem B to problem A?
I know that I can make a DFS tree at height $k$ with repeating vertices, however it solves the problem directly rather than by reduction.