Jumping Fever

Chef has a tree with $N$ nodes (numbered $1$ through $N$). Each node has a value; let's denote the value of node $i$ by $v_i$. Chef likes to travel in this tree. For each pair of nodes $(u, v)$, he defines the score of the path from $u$ to $v$ in the following way: - Suppose that the simple path from node $u$ to node $v$ is a sequence of nodes $u = a_0, a_1, \ldots, a_L = v$, where $L$ is the len