Archi and Tree

Archi is a small boy from Uzhlyandia. For Chef's birthday, he prepared a tree with $N$ vertices (numbered $1$ through $N$). Each edge in this tree has a certain length. There are $M$ speedsters on the tree, numbered $1$ through $M$. For each valid $i$, speedster number $i$ starts at time $t_i$ from vertex number $u_i$ and runs straight to vertex number $v_i$ with constant velocity $s_i$. Before t