Consider a modified version of standard nim game. In this game, there are K piles of stones.There are two players.In each turn a player can remove exactly 1 stone from any of the piles.The winner is who removes the last stone from any of the pile. Note: It is not necessary to remove all stones from all piles.
Lets say distribution of piles is: (1,1).Clearly 1st player will win. For (2,2) 1st player have to remove 1 stone from any of the one pile.Then 2nd player removes remaining one stone and wins.