7 teams will start tournament directly from part 2 (7 is odd number, part 1 will be skipped), were they must play each with other, thus 21 games will be played instead of 7, meanwhile 8 teams will 4 quadfinals, play 2 semifinals, 1 final = 7 games, just much as you need. So, here only one correct answer: 8 teams.

Second case is the same, 67108863 teams will play 2_251_799_713_021_953 games, instead of 67108863.