Interesting Solitaire Game

Question

We have three boxes containing finitely many balls (not already empty). The game consists in "emptying" one of the boxes. The only move allowed is to double the content of a box by transferring balls from a box to another. So in maths $ A,B,C $ box and $|A|=a,|B|=b,|C|=c$. Suppose WLOG $a<b<c \in N$ (natural numbers) (Note that if we pick two equal numbers the game is finished in one move Es $a=5,b=5,c=3 \implies a=10,b=0,c=3$ and the game is over). I do not know the answer but the claim is that for every $(a,b,c)\in N^3$ it is possible to win. But I do not know an elementary and fast proof. Any ideas? P.S. you play alone and move by move starting from an arbitrary configuration.