<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, threshold):
        n = len(nums)

        # Create the modified array
        modified = [math.floor(threshold / float(nums[i])) + 1 for i in range(n)]

        # Printing the modified array for debug (optional)
        for el in modified:
            print(el, end=" ")
        print()

        # Initialize stacks and prefix/suffix arrays
        st = deque()
        pref = [0] * n
        suff = [0] * n

        # Calculate the prefix lengths
        for i in range(n):
            while st and st[-1][0] <= modified[i]:
                st.pop()
            sz = i + 1 if not st else i - st[-1][1]
            pref[i] = sz
            st.append((modified[i], i))

        # Clear the stack for suffix calculation
        st.clear()

        # Calculate the suffix lengths and check the condition
        for i in range(n - 1, -1, -1):
            while st and st[-1][0] <= modified[i]:
                st.pop()
            sz = n - i if not st else st[-1][1] - i
            suff[i] = sz

            # If the condition is met, return the size
            if pref[i] + suff[i] - 1 >= modified[i]:
                return pref[i] + suff[i] - 1

            st.append((modified[i], i))

        # If no valid subarray is found, return -1
        return -1

35100