Can the numbers in nums be sorted into exactly k non-empty groups so that every group's numbers add up to the exact same total? That's the question to answer — yes or no. If the array's total sum doesn't divide evenly by k, the answer is immediately no — there's no target total to aim for. Otherwise, this comes down to trying to fill k running totals to that shared target, one number at a time, backing out of any placement that turns out not to work.