<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 Solution:
    def validSubarraySize(self, nums: List[int], threshold: int) -> int:
        n = len(nums)
        next_s = [n for _ in range(n)]
        prev_s = [-1 for _ in range(n)]
        # 1 3 4 3 1
        #   3 4 3
        #     4
        #   3 4 3
        # 1 3 4 3 1
        stk = deque()  # stores the idx
        # find next_s, non-dec mono stk
        for i, num in enumerate(nums):
            while len(stk) and num < nums[stk[-1]]:
                next_s[stk[-1]] = i
                stk.pop()
            stk.append(i)

        stk.clear()
        for i, num in enumerate(reversed(nums)):
            idx = n - 1 - i
            while len(stk) and num < nums[stk[-1]]:
                prev_s[stk[-1]] = idx
                stk.pop()
            stk.append(idx)

        print(prev_s)
        print(next_s)
        # for p, n in zip(prev_s, next_s):
        #   valid interval is [p + 1, n - 1]
        for i in range(n):
            k = next_s[i] - prev_s[i] - 1
            if nums[i] > threshold / k:
                return k

        return -1
31500