<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]:
        
        def update(index, val, tree, size):
            index += size
            tree[index] += val

            while index > 1:
                index //= 2
                tree[index] = tree[index * 2] + tree[index * 2 + 1]
            
        def query(left, right, tree, size):
            left += size
            right += size
            curSum = 0

            while left < right:
                if left % 2 == 1:
                    curSum += tree[left]
                    left += 1

                if right % 2 == 1:
                    right -= 1
                    curSum += tree[right]
                
                left //= 2
                right //= 2
            
            return curSum
        
        offset = 10 ** 4
        size = 2 * 10 ** 4 + 1
        tree = [0] * 2 * size
        res = []

        for num in reversed(nums):
            countSmaller = query(0, num + offset, tree, size)
            res.append(countSmaller)
            update(num + offset, 1, tree, size)
        
        return reversed(res)


33893