<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
        for n in nums[::-1]:
            i = n + N
            s = 0
            while i > 0:
                s += tree[i]
                i -= i & -i
            res.append(s)
            
            i = n + N + 1
            while i < M:
                tree[i] += 1
                i += i & -i
        return res[::-1]

        # 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)

        #     i = M + n
        #     tree[i] += 1
        #     while i > 1:
        #         i //= 2
        #         tree[i] = tree[i * 2] + tree[i * 2 + 1]
        # return res[::-1]

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