<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 NumArray:

    def __init__(self, nums: List[int]):
        self.n = len(nums)
        self.tree = [0] * 2 * self.n

    def update(self, index: int, val: int) -> None:
        index += self.n
        self.tree[index] += val
        while index:
            left = right = index
            if index % 2:
                left -= 1
            else:
                right += 1
            self.tree[index // 2] = self.tree[left] + self.tree[right]
            index //= 2

    def sumRange(self, left: int, right: int) -> int:
        # Find the sum in the range [left+n, right+n] in the tree
        left += self.n
        right += self.n
        res = 0
        while left <= right:
            if left % 2 == 1:
                res += self.tree[left]
                left += 1
            if right % 2 == 0:
                res += self.tree[right]
                right -= 1
            left //= 2
            right //= 2
        return res


class Solution:
    def countSmaller(self, nums: List[int]) -> List[int]:
        m = {}
        for i, v in enumerate(sorted(set(nums))):
            m[v] = i
        ans = []
        fenwick = NumArray(m)
        for n in reversed(nums):
            ans.append(fenwick.sumRange(0, m[n] - 1))
            fenwick.update(m[n], 1)
        return reversed(ans)

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