<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 = []
        N = 10 ** 4
        M = N * 2 + 1
        tree = [0] * (M * 2)
        for n in nums[::-1]:
            n += N
            s = 0
            l = M
            r = M + n - 1
            while l <= r:
                if l % 2 == 1:
                    s += tree[l]
                    l += 1
                l //= 2
                if r % 2 == 0:
                    s += tree[r]
                    r -= 1
                r //= 2
            res.append(s)
            # print('###', n, l, r)

            i = M + n
            tree[i] += 1
            # print('###', n, i, tree)
            while i > 1:
                i //= 2
                tree[i] = tree[i * 2] + tree[i * 2 + 1]
                # print('###', n, i, tree)
            # print('@@@', tree[l], tree[r])
            # print(tree)
        return res[::-1]



        # # implement segment tree
        # def update(index, value, tree, size):
        #     index += size  # shift the index to the leaf
        #     # update from leaf to root
        #     tree[index] += value
        #     while index > 1:
        #         index //= 2
        #         tree[index] = tree[index * 2] + tree[index * 2 + 1]

        # def query(left, right, tree, size):
        #     # return sum of [left, right)
        #     result = 0
        #     left += size  # shift the index to the leaf
        #     right += size
        #     while left < right:
        #         # if left is a right node
        #         # bring the value and move to parent's right node
        #         if left % 2 == 1:
        #             result += tree[left]
        #             left += 1
        #         # else directly move to parent
        #         left //= 2
        #         # if right is a right node
        #         # bring the value of the left node and move to parent
        #         if right % 2 == 1:
        #             right -= 1
        #             result += tree[right]
        #         # else directly move to parent
        #         right //= 2
        #     return result

        # offset = 10**4  # offset negative to non-negative
        # size = 2 * 10**4 + 1  # total possible values in nums
        # tree = [0] * (2 * size)
        # result = []
        # for num in reversed(nums):
        #     smaller_count = query(0, num + offset, tree, size)
        #     result.append(smaller_count)
        #     update(num + offset, 1, tree, size)
        # return reversed(result)
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