<p>Given an integer array <code>nums</code>, return<em> an integer array </em><code>counts</code><em> where </em><code>counts[i]</code><em> is the number of smaller elements to the right of </em><code>nums[i]</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [5,2,6,1]
<strong>Output:</strong> [2,1,1,0]
<strong>Explanation:</strong>
To the right of 5 there are <b>2</b> smaller elements (2 and 1).
To the right of 2 there is only <b>1</b> smaller element (1).
To the right of 6 there is <b>1</b> smaller element (1).
To the right of 1 there is <b>0</b> smaller element.
</pre>

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

<pre>
<strong>Input:</strong> nums = [-1]
<strong>Output:</strong> [0]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [-1,-1]
<strong>Output:</strong> [0,0]
</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>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def countSmaller(self, nums: List[int]) -> List[int]:
        offset = 10**4
        size = 2 * 10**4 + 1
        tree = [0] * (4 * size)
        result = []

        def update(index, value, node=1, node_left=0, node_right=size-1):
            if node_left == node_right:
                tree[node] += value
                return
            
            mid = (node_left + node_right) // 2

            if index <= mid:
                update(index, value, node * 2, node_left, mid)
            else:
                update(index, value, node * 2 + 1, mid + 1, node_right)

            tree[node] = tree[node * 2] + tree[node * 2 + 1]

        def query(left, right, node=1, node_left=0, node_right=size-1):
            if right < node_left or left > node_right:
                return 0
            if left <= node_left and node_right <= right:
                return tree[node]
            
            mid = (node_left + node_right) // 2
            left_result = query(left, right, node * 2, node_left, mid)
            right_result = query(left, right, node * 2 + 1, mid + 1, node_right)

            return left_result + right_result

        for num in reversed(nums):
            smaller_count = query(0, num + offset - 1, 1, 0, size-1)
            result.append(smaller_count)
            update(num + offset, 1, 1, 0, size-1)

        return list(reversed(result))
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