Tree Tag

Two players, Alice and Bob, play a pursuit-evasion game on an undirected tree with n nodes numbered from 0 to n-1. Alice starts at node a, Bob starts at node b. Alice moves first. On each turn, a player may move along the tree edges up to a maximum distance: Alice can traverse at most da edges, Bob at most db edges. A player may also choose to stay in place. Alice catches Bob if she occupies the same node as Bob after her move. If Alice can force a capture within a finite number of turns, she wins; otherwise Bob wins. Both players play optimally. Determine whether Alice can force a win.

Examples
Input: [3,0,2,2,1,[[0,1],[1,2]]]
Output: true
Hints

Tree Tag

Two players, Alice and Bob, play a pursuit-evasion game on an undirected tree with n nodes numbered from 0 to n-1. Alice starts at node a, Bob starts at node b. Alice moves first. On each turn, a player may move along the tree edges up to a maximum distance: Alice can traverse at most da edges, Bob at most db edges. A player may also choose to stay in place. Alice catches Bob if she occupies the same node as Bob after her move. If Alice can force a capture within a finite number of turns, she wins; otherwise Bob wins. Both players play optimally. Determine whether Alice can force a win.