Batman and Tree

Nazik gave Batman a tree with $N$ vertices (numbered $1$ through $N$). There are some robbers in the tree; of course, Batman wants to catch the robbers. Initially, Batman is in a vertex $s$ and his power is equal to $p$. During each of the next $M$ seconds, the following process happens: - A robber with power $r$ runs from a vertex $x$ straight to vertex $y$. - Batman either catches the robber or