You are playing a game with a robot. The game starts with two integers: A and M. The robot makes exactly one move in the entire game, and it does so at the very beginning - it will remove exactly 1 digit from A and output it as the starting value (say X). Note that the value A remains intact. It is not changed by the robot. After the robot makes its moves, it is your turn. You can make an unlimited number of moves. In each move, you must remove exactly 1 digit from A and append it to X (to the right side of X). Again note that none of your moves change the value of A. You win if you can eventually make X a multiple of M (i.e. X mod M = 0). How many possible starting moves bot can make such that you are guaranteed to win assuming you play optimally?