3669 - Balanced K-Factor Decomposition.

Medium

Given two integers n and k, split the number n into exactly k positive integers such that the product of these integers is equal to n.

Return any one split in which the maximum difference between any two numbers is minimized. You may return the result in any order.

Example 1:

Input: n = 100, k = 2

Output: 10,10

Explanation:

The split [10, 10] yields 10 * 10 = 100 and a max-min difference of 0, which is minimal.

Example 2:

Input: n = 44, k = 3

Output: 2,2,11

Explanation:

• Split [1, 1, 44] yields a difference of 43

• Split [1, 2, 22] yields a difference of 21

• Split [1, 4, 11] yields a difference of 10

• Split [2, 2, 11] yields a difference of 9

Therefore, [2, 2, 11] is the optimal split with the smallest difference 9.

Constraints:

• <code>4 <= n <= 10⁵</code>

• 2 <= k <= 5

• k is strictly less than the total number of positive divisors of n.