<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]:
        div = self.find_divisors(num+1) + self.find_divisors(num+2)
        abv = {(x,y):abs(x-y) for x,y in div }

        least = float('inf')
        least_key = None
        for key, value in abv.items():
            if value < least: 
                least = value
                least_key = key
            
        return [least_key[0],least_key[1]]


    def find_divisors(self, num:int) -> List[tuple]: 
        list=[]
        for x in range(int((num**(1/2))//1+1)): 
            if x is not 0 and num % x == 0:
                list.append((x,int(num/x)))
        return list
                
        
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