Given a directed graph G = (V, E) and a pair of vertices s, t in G, the Hamiltonian Path problem asks whether there is a simple path from s to t that visits every vertex of G exactly once. The Hamiltonian Cycle problem asks if there is a cycle in a directed graph G that visits every vertex exactly once. Show that Hamiltonian Path and Hamiltonian Cycle problems are polynomial-time reducible to each other.