P-010 Tipping the Buckets

There are three buckets containing m, n, p integral units of water respectively. You can repeatedly perform the following step: transfer water from one bucket to another such that the amount of water in the other bucket is exactly doubled. For example, if m < n, transferring m units will result in the buckets containing m and n units ending up with 2m and n-m units. Each bucket has a sufficient capacity > m+n+p.
Show that it is always possible to get one bucket empty.

Note – this puzzle is harder than the older three bucket puzzle where the receipient bucket is to be filled to the brim.