<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]:
        class BIT:  # 0-indexed.
            def __init__(self, n):
                self.__bit = [0] * (n + 1)  # Extra one for dummy node.

            def add(self, i, val):
                i += 1  # Extra one for dummy node.
                while i < len(self.__bit):
                    self.__bit[i] += val
                    i += i & -i

            def query(self, i):
                i += 1  # Extra one for dummy node.
                ret = 0
                while i > 0:
                    ret += self.__bit[i]
                    i -= i & -i
                return ret

        # Get the place (position in the ascending order) of each number.
        sorted_nums = sorted(zip(nums, range(len(nums))))
        lookup = {i: new_i for new_i, (_, i) in enumerate(sorted_nums)}

        # Count the smaller elements after the number.
        result, bit = [0] * len(nums), BIT(len(nums))
        for i in reversed(range(len(nums))):
            result[i] = bit.query(lookup[i] - 1)
            bit.add(lookup[i], 1)
        return result

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