Heap Stones

Problem description. There are N piles of stones where the ith pile has Xi stones in it. Alice and Bob play the following game: Alice starts, and they alternate turns. In a turn, a player can choose any one of the piles of stones and divide the stones in it into any number of unequal piles such that no two of the newly created piles have the same number of stones. For example, if there 8 stones