Partition array into K subsets, each with balanced sum
Use dynamic programming.  This is a straightforward application of dynamic programming.  This is a very nice exercise, so I'll let you do the exercise yourself and won't spoil it for you -- but since you only wanted a hint, my hint is "use dynamic programming" (that's a huge, enormous hint that should be enough for you to work out the rest of the details).

In particular, you should be able to solve this in $O(kn^2)$ time.