Selinas the Chefs Falling on the Tree

You are given a tree with $N$ nodes numbered $1$ through $N$, rooted at node $1$. There are many really good ingredients on this tree, so $M$ chefs Selinas are going to pick them all up. For each $i$ ($1 \le i \le M$), the $i$-th Selina will start falling from the root in the $t_i$-th second. Obviously, Selinas can only move in two directions — from each node, a Selina can *fall* to one of its ch