Maximize It

You are given a sequence of $N$ powers of an integer $k$; let's denote the $i$-th of these powers by $k^{A_i}$. You should partition this sequence into two non-empty **contiguous** subsequences; each element of the original sequence should appear in exactly one of these subsequences. In addition, the product of (the sum of elements of the left subsequence) and (the sum of elements of the right sub