Bucket Game

There are $N$ Buckets where $i^{th}$ bucket contains $A_i$ balls initially. Alice and Bob decided to play a game with following rules. Both players take turns with Alice going first: - If there are no balls left, the game ends. - In his/her turn, the player will remove a ball from any bucket which contains **at least** one ball. - If, after the move, the bucket from which the ball is removed bec