SP11414 COT3 - Combat on a tree

Alice and Bob are playing a game on a tree of n nodes.Each node is either black or white initially. They take turns to do the following operation: Choose a white node v from the current tree; Color all white nodes on Path(1,v) to black. The player who takes the last turn wins. Now Alice takes the first turn.Help her find out if she can win when they both use optimal strategy.

The first line of input contains a integer n representing the number of nodes in the tree. 1

If Alice can't win print -1. Otherwise determine all the nodes she can choose in the first turn in order to win.Print them in ascending order.