Statement

William is a long-time expert in drinking games, and today he invented a fantastic game! He starts with two glasses of different capacities A_C and B_C containing some amount of apple juice. The only valid operations are the following: (1) Drink all the apple juice contained in one of the glasses. (2) Refill one of the glasses completely (regardless of how full it is already). (3) Pour a glass into another until either the other glass is full or the first glass is empty. William chose a "starting configuration" (A_S, B_S) and he is now challenging Giorgio to reach a "goal configuration" (A_G, B_G), by strictly following the rules of the game. Giorgio doesn't want to drink too much apple juice (or spend a lot of time pouring, for that matter): help him reach the goal configuration in the least possible number of steps!