Maximum Equal Sum K Subsequences Given an array we need to find maximum equal sum $K$ subsequences, i.e. we want the sum to be maximized such that there are exactly $K$ non-overlapping subsequences each having the same sum.
Example: 

A = [1, 2, 3, 4, 6] &amp; K = 2
Maximum Sum Subsequence = 8 = [2, 6] &amp; [1, 3, 4]

If, K = 3 and A = [1, 2, 3, 4, 6, 8, 9]
Maximum Sum Subsequence = 11 = [9, 2] &amp; [8, 3] &amp; [6, 4, 1]


It is not necessary that all the elements of the array need to be a part of the subsequences but each element can only be part of 1 subsequence.

I tried a brute force approach with Knapsack but that doesnt work. 
Any better approaches or optimizations?
This problem is NP-complete by reduction to the given subset sum problem, which asks if there is a subset $S$ from a set with a certain sum $n$.

Suppose we are given such an instance and that your problem can be efficiently solved. Then we can transform the instance by making $S' = S \cup \{x, x - n\}$ for some sufficiently large $x$ and solving your problem to find the $K = 2$ maximum equal subsequence sums. Then iff the answer includes $x$ and $x - n$ there is a subset that sums to $n$ and we efficiently solved the given subset sum problem.