Succinct bounded-sum array with $O(1)$ access
Raman, Raman, and Rao is a standard reference for rank/select in O(1) time.  This solves your problem for the special case of a static array, i.e., you can retrieve $A[i]$ in $O(1)$ time, but not update $A$: see the third bullet item in their abstract.  The rank operation can be used to determine membership, and the select operation retrieves the $i$th element of the array.  Their data structure requires $o(n)+O(\lg \lg m)$ extra space beyond the minimum.

The conclusion of their paper also mentions a lower bound if you want to support insert, delete, rank, and select.  I don't know if that's applicable here.