<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 findClosestDivisors(target):
            min_diff = float('inf')
            closest_pair = (1, target)
            
            # Check divisors from 1 to sqrt(target)
            i = 1
            while i * i <= target:
                if target % i == 0:
                    j = target // i
                    # Calculate the difference
                    diff = abs(i - j)
                    # Update closest pair if the current pair is closer
                    if diff < min_diff:
                        min_diff = diff
                        closest_pair = (i, j)
                i += 1
            
            return closest_pair
        
        # Calculate targets
        target1 = num + 1
        target2 = num + 2
        
        # Find closest divisors for both targets
        pair1 = findClosestDivisors(target1)
        pair2 = findClosestDivisors(target2)
        
        # Find the pair with the smallest difference
        if abs(pair1[0] - pair1[1]) < abs(pair2[0] - pair2[1]):
            return list(pair1)
        else:
            return list(pair2)
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