Die Hard - 3 Jugs

See the problem 368 by Philippe. This time we have 3 jugs with capacities 7, 31 and 1048575. What are the gallons that require the most number of moves? Answer format: moves,g₁,g₂,... where g_i-1 < g_i Example: 20,54,57,58,62,66,67,70 if we have 3, 7 and 127 gallon jugs [My timing < 1m and my memory requirement < 100M]