Tree Walk

There are two people walking along a tree with $N$ nodes (numbered $1$ through $N$), each of them with speed 1 edge per second. The walk of the first person is described by a sequence of nodes $u_1, u_2, \dots, u_K$. This person appears in node $u_1$ at time $0$ and walks to node $u_2$ using the shortest **path**; then, immediately after reaching $u_2$, walks to node $u_3$ using the shortest pa