different menu for different membership levels

Hello expert,
I created 3 levels of memberships, free, member and premium. And I want each membership has its own menu, so I assign different menu to different membership at the access level.

The problem is that when I logged in as free membership, there was NO menu's showing up at all because the default menu was at premium membership level.

How can I have different menu shows up for each membership level?
Any advice? can I accomplish this?

Thank you very much