2178 - Maximum Split of Positive Even Integers.

Medium

You are given an integer finalSum. Split it into a sum of a maximum number of unique positive even integers.

• For example, given finalSum = 12, the following splits are valid (unique positive even integers summing up to finalSum): (12), (2 + 10), (2 + 4 + 6), and (4 + 8). Among them, (2 + 4 + 6) contains the maximum number of integers. Note that finalSum cannot be split into (2 + 2 + 4 + 4) as all the numbers should be unique.

Return a list of integers that represent a valid split containing a maximum number of integers. If no valid split exists for finalSum, return an empty list. You may return the integers in any order.

Example 1:

Input: finalSum = 12

Output: 2,4,6

Explanation: The following are valid splits: (12), (2 + 10), (2 + 4 + 6), and (4 + 8).

(2 + 4 + 6) has the maximum number of integers, which is 3. Thus, we return 2,4,6.

Note that 2,6,4, 6,2,4, etc. are also accepted.

Example 2:

Input: finalSum = 7

Output: []

Explanation: There are no valid splits for the given finalSum. Thus, we return an empty array.

Example 3:

Input: finalSum = 28

Output: 6,8,2,12

Explanation: The following are valid splits: (2 + 26), (6 + 8 + 2 + 12), and (4 + 24).

(6 + 8 + 2 + 12) has the maximum number of integers, which is 4. Thus, we return 6,8,2,12.

Note that 10,2,4,12, 6,2,4,16, etc. are also accepted.

Constraints:

• <code>1 <= finalSum <= 10¹⁰</code>