The World but this would be incredibly bloody and hopefully never occurs. Also you forgot India? Whose side are they on? They have the third or fourth largest military so they could be a major contributor to either side.
..and Brazil for that matter. Both nations have some ability to project power. (although Italy spends more than both on defense)
Ah yes Brazil, who's side they fall under will probably be the deciding factor in Latin America in this hypothetical scenario without the use of nuclear weapons.