The Shakuni Game

Shakuni, fond of playing manipulative games is playing one with Yudhishthir. Shakuni has given Yudhishthir $N$ stones and asked him to repeat the following operation until $NN$ becomes $11$: - Choose an integer $XX$ such that $X \geq 1$ and $X$ is a divisor of $N$, and then divides $N$ by $X$ (the new value of $N$ becomes $N/X$). If $X$ is even, Yudhishthir gets $A$ points, otherwise he gets $B$