<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]:
        res = [0] * len(nums)
        shift = 0
        max_num = -2e4
        for value in nums:
            max_num = max(max_num, value)
            if value <=0 and abs(value) + 1 > shift:
                shift = abs(value) + 1

        bit = BIT(max_num+shift)
        for value in nums:
            bit.update(value+shift, 1)      

        for idx, value in enumerate(nums):
            bit.update(value+shift, -1)  

            res[idx] = bit.sum(value+shift-1)

        return res

class BIT:

    def __init__(self, size):
        self.bit = [0] * (size + 1)

    def sum(self, idx):
        res = 0

        while idx > 0:
            res += self.bit[idx]

            idx -= idx & (-idx)

        return res

    def update(self, idx, value):

        while idx < len(self.bit):
            self.bit[idx] += value   
            idx += idx & (-idx)

        
1603