<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>

def find_any_subarray_size(nums, threshold):
    n = len(nums)
    nums.append(0)  # Sentinel value to handle NSE
    prev_smaller = [-1] * n
    next_smaller = [n] * n

    # Monotonic stack for PSE
    stack = []
    for i in range(n):
        while stack and nums[stack[-1]] >= nums[i]:
            stack.pop()
        prev_smaller[i] = stack[-1] if stack else -1
        stack.append(i)

    # Monotonic stack for NSE
    stack = []
    for i in range(n - 1, -1, -1):
        while stack and nums[stack[-1]] >= nums[i]:
            stack.pop()
        next_smaller[i] = stack[-1] if stack else n
        stack.append(i)

    nums.pop()  # Remove the sentinel value

    # Initialize maxMins array
    maxMins = [0] * (n + 2)
    for i in range(n):
        length = next_smaller[i] - prev_smaller[i] - 1
        maxMins[length] = max(maxMins[length], nums[i])

    # Propagate maximum values backwards
    for k in range(n - 1, 0, -1):
        maxMins[k] = max(maxMins[k], maxMins[k + 1])

    # Find any valid subarray length
    for k in range(1, n + 1):
        if maxMins[k] * k > threshold:
            return k
    return -1
class Solution:


    def validSubarraySize(self, nums: List[int], threshold: int) -> int:
        return find_any_subarray_size(nums, threshold)
        
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