<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]:
        BIT = [0] * 20001


        tree = BinaryIndexTree(BIT)

        ans = []
        for n in reversed(nums):
            ans.append(tree.getPrefixSum(n+9999))
            tree.update(n+10000, tree.arr[n+10000]+1)
        return reversed(ans)



        
class BinaryIndexTree:
    def __init__(self, nums) -> None:
        self.nLen = len(nums)
        self.tree = [0] * (self.nLen + 1)  # BIT
        self.arr = [0] * self.nLen  # 原始數據

        for i in range(self.nLen):
            bitIndex = i + 1
            self.tree[bitIndex] += nums[i]
            self.arr[i] = nums[i]
            parent = bitIndex + (bitIndex & -bitIndex)
            if parent < self.nLen:
                self.tree[parent] += self.tree[bitIndex]
    
    def update(self, index, value):
        difference = value - self.arr[index]
        self.arr[index] = value
        index += 1
        while index < self.nLen:
            self.tree[index] += difference
            index += (index & -index)

    def getPrefixSum(self, index):
        prefixSum = 0
        index += 1
        while index > 0:
            prefixSum += self.tree[index]
            index -= (index & -index)
        return prefixSum
    
    def getRangeSum(self, start, end):
        return self.getPrefixSum(end) - self.getPrefixSum(start)
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