<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 Bit:

    def __init__(self, n: int) -> None:
        self.bit = [0 for _ in range(n + 1)]

    def update(self, i: int, val: int) -> None:
        i += 1
        while i < len(self.bit):
            self.bit[i] += val
            i += self._find_RSB(i)

    def prefix_sum(self, i: int) -> int:
        i += 1
        s = 0
        while i > 0:
            s += self.bit[i]
            i -= self._find_RSB(i)
        return s

    def _find_RSB(self, i: int) -> int:
        return i & -i


class Solution:
    def countSmaller(self, nums: List[int]) -> List[int]:
        counts = []
        shift = 10 ** 4
        bit = Bit(max(nums) + shift)
        for i in range(len(nums) - 1, -1, -1):
            counts.append(bit.prefix_sum(nums[i] + shift - 1))
            bit.update(nums[i] + shift, 1)
        return counts[::-1]
1558