<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_closest_divisors(target: int) -> List[int]:
            min_diff = float('inf')
            result = []
            i = 1
            while i * i <= target:
                if target % i == 0:
                    divisor1 = i
                    divisor2 = target // i
                    if abs(divisor1 - divisor2) < min_diff:
                        min_diff = abs(divisor1 - divisor2)
                        result = [divisor1, divisor2]
                i += 1
            return result

        plus_one_divisors = find_closest_divisors(num + 1)
        plus_two_divisors = find_closest_divisors(num + 2)

        if abs(plus_one_divisors[0] - plus_one_divisors[1]) <= abs(plus_two_divisors[0] - plus_two_divisors[1]):
            return plus_one_divisors
        else:
            return plus_two_divisors
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