# How can I combine 2 PDA’s into 1

I need to form PDA for this language: {$$a^nb^m|n=m \vee n=2m$$}

I know the idea of building each one separately but how do I combine them into 1 PDA?

LHS: for every ‘a’ I push ‘A’ inside stack and for every ‘b’ I eject ‘A’.

RHS:for every ‘a’ I push ‘A’ inside stack and for every ‘b’ I eject 2 times ‘A’.

How can I combine them? Can I somehow use non determinism?