<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>

class Solution:
    def closestDivisors(self, num: int) -> List[int]:
        def find_divisors(n):
            divisors = []
            i = 1
            while i * i <= n:
                if n % i == 0:
                    divisors.append((i, n // i))
                i += 1
            return divisors
        
        # Find divisors for num + 1 and num + 2
        divisors_plus_one = find_divisors(num + 1)
        divisors_plus_two = find_divisors(num + 2)
        
        # Initialize the result with the first pair from num + 1
        result = min(divisors_plus_one, key=lambda x: abs(x[0] - x[1]))
        
        # Compare with pairs from num + 2
        for pair in divisors_plus_two:
            if abs(pair[0] - pair[1]) < abs(result[0] - result[1]):
                result = pair
        
        # Return the pair with the smallest difference
        return list(result)

# 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]
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