human
What is a Python program to find the closest two integers in absolute difference whose product equals num + 1 or num + 2 given the following:
I found an interesting problem on https://leetcode.com/problems/closest-divisors/:
Given an integer num, find the closest two integers in absolute difference whose product equals num + 1 or num + 2.
Return the two integers in any order.
 
Example 1:
Input: num = 8
Output: [3,3]
Explanation: For num + 1 = 9, the closest divisors are 3 & 3, for num + 2 = 10, the closest divisors are 2 & 5, hence 3 & 3 is chosen.

Example 2:
Input: num = 123
Output: [5,25]

Example 3:
Input: num = 999
Output: [40,25]

 
Constraints:

1 <= num <= 10^9

I tried it in Python, but could not do it. Can you solve it?
assistant
#Here is Python program to find the closest two integers in absolute difference whose product equals num + 1 or num + 2.

class Solution:
    def closestDivisors(self, num: int) -> List[int]:
        ans = num + 1
        val = None
        for i in range(1, ceil(sqrt(num+3))):
            if (num + 1) % i == 0:
                j = (num + 1) // i
                if abs(i-j) <= ans:
                    ans = abs(i-j)
                    val = [i, j]
            if (num + 2) % i == 0:
                j = (num + 2) // i
                if abs(i-j) <= ans:
                    ans = abs(i-j)
                    val = [i, j]
        return val