Game of Stones

Sam and Zuck are playing a game. In this game there are k piles, numbered from 1 to n. Each pile, for i from 1 to n, has ni number of stones. In his turn, a player can select any odd number of piles having at least one stone, and remove one stone each from all these piles. Since Zuck already is the owner of a multi-billion dollar company, he allows Sam to take the first turn in this game. The play