<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]:
        # if len(nums) <1:
        #     return []
        # arr = []
        # res = []
        # for num in nums[::-1]:
        #     index = bisect.bisect_left(arr, num)
        #     res.append(index)
        #     arr.insert(index, num)
        # #  O(N^2)
        # return res[::-1]
        sorted_nums = sorted(set(nums))
        rank = {num: i+1 for i, num in enumerate(sorted_nums)} # 1-based index
        
        n = len(nums)
        res = []
        bit = BIT(len(sorted_nums))
        
        for num in reversed(nums):
            # Get how many numbers are smaller than the current number
            pos = rank[num]
            res.append(bit.query(pos - 1))
            # Add the current number to the BIT
            bit.update(pos, 1)
        
        return res[::-1]


class BIT:
    def __init__(self, n):
        self.size = n
        self.tree = [0] * (n + 1)
    
    def update(self, idx, value):
        while idx <= self.size:
            self.tree[idx] += value
            idx += idx & -idx
    
    def query(self, idx):
        sum = 0
        while idx > 0:
            sum += self.tree[idx]
            idx -= idx & -idx
        return sum

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