Another version of the game of NIM: Th ere is a version of the game of NIM different from what is described in Example 11.10. Here, instead of a number of piles, the game starts with a single pile of an odd number of sticks. During the game, each player in his turn has to split a pile into two. Th e two piles thus created should consist of unequal number of sticks. Th ere must be at least one stick in each pile. Th e game terminates when a player have no valid move. Th e player who fails to make a move loses the game and the other player wins. Construct the complete game tree for NIM (7), i.e., the game which starts with 7 sticks in a single pile.