<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>

inline constexpr int MAX_M = 1e4, MIN_M = -1e4, HIGH = MAX_M - MIN_M, MAX_N = 1e5;
inline constinit int fenwick[HIGH + 1]{}, saved[MAX_N]{}, saved_pos = 0;

class Solution {
public:
    Solution() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); }
    vector<int> countSmaller(vector<int>& nums) {
        int max_m = nums[0], min_m = nums[0];
        for (int x : nums) {
            if (x > max_m) {
                max_m = x;
            } else if (x < min_m) {
                min_m = x;
            }
        }
        int high = max_m - min_m;

        vector<int> ans = std::move(nums);
        for (int i = ans.size() - 1, v; i >= 0; --i) {
            v = saved[saved_pos++] = ans[i];
            ans[i] = 0;
            for (int j = v - 1 - min_m + 1; j >= 1; j -= (j & -j)) {
                ans[i] += fenwick[j - 1];
            }
            for (int j = v - min_m + 1; j <= high; j += (j & -j)) {
                ++fenwick[j - 1];
            }
        }

        while (saved_pos) {
            for (int j = saved[--saved_pos] - min_m + 1; j <= high; j += (j & -j)) {
                --fenwick[j - 1];
            }
        }
        
        return ans;
    }
};
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