Two players take turns by breaking an m x n chocolate bar. The chocolate bar has one spoiled one-by-one square. Each break needs to be a single straight line cutting all the way cross the bar along the boundaries between the squares. After each break, the player who broke the bar last eats the piece that does not contain the spoiled corner. The player left with the spoiled square loses.

a) Is it better to go first or second in this game? Why?

b) Write an interactive program to play this game on the computer. Your program should make a winning move in a winning position and a random legitimate move in a losing position.