<p>You are given an integer array <code>nums</code> and an integer <code>threshold</code>.</p>

<p>Find any subarray of <code>nums</code> of length <code>k</code> such that <strong>every</strong> element in the subarray is <strong>greater</strong> than <code>threshold / k</code>.</p>

<p>Return<em> the <strong>size</strong> of <strong>any</strong> such subarray</em>. If there is no such subarray, return <code>-1</code>.</p>

<p>A <strong>subarray</strong> is a contiguous non-empty sequence of elements within an array.</p>

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

<pre>
<strong>Input:</strong> nums = [1,3,4,3,1], threshold = 6
<strong>Output:</strong> 3
<strong>Explanation:</strong> The subarray [3,4,3] has a size of 3, and every element is greater than 6 / 3 = 2.
Note that this is the only valid subarray.
</pre>

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

<pre>
<strong>Input:</strong> nums = [6,5,6,5,8], threshold = 7
<strong>Output:</strong> 1
<strong>Explanation:</strong> The subarray [8] has a size of 1, and 8 &gt; 7 / 1 = 7. So 1 is returned.
Note that the subarray [6,5] has a size of 2, and every element is greater than 7 / 2 = 3.5. 
Similarly, the subarrays [6,5,6], [6,5,6,5], [6,5,6,5,8] also satisfy the given conditions.
Therefore, 2, 3, 4, or 5 may also be returned.</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i], threshold &lt;= 10<sup>9</sup></code></li>
</ul>

class UnionFind:
    def __init__(self, n):
        self.parents = [i for i in range(n)]
        self.sizes = [1 for _ in range(n)]
    
    def find(self, n):
        if self.parents[n] != n:
            self.parents[n] = self.find(self.parents[n])
        return self.parents[n]

    def union(self, n1, n2):
        if self.size(n1) < self.size(n2):
            self.union(n2, n1)
            return
        parent1 = self.find(n1)
        parent2 = self.find(n2)
        self.parents[parent2] = parent1
        self.sizes[parent1] += self.sizes[parent2]
    
    def size(self, n):
        return self.sizes[self.find(n)]
    
class Solution:
    def validSubarraySize(self, nums: List[int], threshold: int) -> int:
        arr = []
        uf = UnionFind(len(nums))

        for i, n in enumerate(nums):
            arr.append((n, i))

        processed = set()
        
        arr.sort(reverse=True)

        for n, i in arr:
            if i - 1 in processed:
                uf.union(i - 1, i)
            if i + 1 in processed:
                uf.union(i, i + 1)
            processed.add(i)
            if n > threshold / uf.size(i):
                return uf.size(i)
        return -1
            
            
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