<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]:
        memo = {}
        nums.sort()
        n = len(nums)

        def generateSubsets(i, prev):
            key = (i,prev)
            if key in memo:
                return memo[key]
            if i == n:
                return []
            res1 = generateSubsets(i+1, prev)
            res2 = []
            if not prev or nums[i] % prev == 0:
                res2 = [nums[i]] + generateSubsets(i+1, nums[i])
            res = res1 if len(res1) > len(res2) else res2
            memo[key] = res
            return res
        return generateSubsets(0, None)
        



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