<p>Given an integer <code>num</code>, find the closest two integers in absolute difference whose product equals&nbsp;<code>num + 1</code>&nbsp;or <code>num + 2</code>.</p>

<p>Return the two integers in any order.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> num = 8
<strong>Output:</strong> [3,3]
<strong>Explanation:</strong> For num + 1 = 9, the closest divisors are 3 &amp; 3, for num + 2 = 10, the closest divisors are 2 &amp; 5, hence 3 &amp; 3 is chosen.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> num = 123
<strong>Output:</strong> [5,25]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> num = 999
<strong>Output:</strong> [40,25]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num &lt;= 10^9</code></li>
</ul>

from typing import List
import math

class Solution:
    def closestDivisors(self, num: int) -> List[int]:
        def find_closest_divisors(n: int) -> List[int]:
            closest_pair = [1, n]
            min_diff = n - 1
            for i in range(1, int(math.sqrt(n)) + 1):
                if n % i == 0:
                    j = n // i
                    if abs(i - j) < min_diff:
                        closest_pair = [i, j]
                        min_diff = abs(i - j)
            return closest_pair
        
        # Check for num + 1
        closest1 = find_closest_divisors(num + 1)
        # Check for num + 2
        closest2 = find_closest_divisors(num + 2)
        
        # Compare which pair has the smallest difference
        if abs(closest1[0] - closest1[1]) <= abs(closest2[0] - closest2[1]):
            return closest1
        else:
            return closest2

# Example usage:
# solution = Solution()
# print(solution.closestDivisors(8))  # Output: [3, 3]
# print(solution.closestDivisors(123))  # Output: [5, 25]
# print(solution.closestDivisors(999))  # Output: [40, 25]
156