Prove that if $A,B$ are finite Abelian groups and for every $n$ they have the same amount of elements of order $n$, then $A \simeq B$

Question

Prove that if $A,B$ are finite Abelian groups and for every $n$ they have the same amount of elements of order $n$, then $A \simeq B$.

I know I have to use primary decomposition, but am not sure how exactly. Any guidance would be appreciated!