<p>Given a set of <strong>distinct</strong> positive integers <code>nums</code>, return the largest subset <code>answer</code> such that every pair <code>(answer[i], answer[j])</code> of elements in this subset satisfies:</p>

<ul>
	<li><code>answer[i] % answer[j] == 0</code>, or</li>
	<li><code>answer[j] % answer[i] == 0</code></li>
</ul>

<p>If there are multiple solutions, return any of them.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3]
<strong>Output:</strong> [1,2]
<strong>Explanation:</strong> [1,3] is also accepted.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,4,8]
<strong>Output:</strong> [1,2,4,8]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 2 * 10<sup>9</sup></code></li>
	<li>All the integers in <code>nums</code> are <strong>unique</strong>.</li>
</ul>

class Solution:
    def largestDivisibleSubset(self, nums: List[int]) -> List[int]:
        nums.sort()

        @cache
        def largest_subset(latest_num: Optional[int], start: int) -> List[int]:
            if start >= len(nums):
                return []
            cur_num = nums[start]
            is_divisible = True
            if latest_num:
                is_divisible = cur_num % latest_num == 0
            if is_divisible:
                take = largest_subset(cur_num, start + 1)
                not_take = largest_subset(latest_num, start + 1)
                return (
                    [cur_num] + take
                    if len(take) + 1 >= len(not_take)
                    else not_take
                )
            else:
                return largest_subset(latest_num, start + 1)

        return largest_subset(None, 0)
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