<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 {
private:
    int n;
    unordered_map<int,int> segt;
    void update(int index, int val) {
        int l = 0, r = n-1, i = 0, m;
        // cout<<"index = "<<index<<endl;
        while(l < r) {
            // cout<<"l = "<<l<<", r = "<<r<<", i = "<<i<<endl;
            segt[i] += val;
            // cout<<"val = "<<segt[i]<<endl;
            m = (l+r)/2;
            if(index <= m){
                r = m;
                i = 2*i + 1;
            }else{
                l = m + 1;
                i = 2*i + 2;
            }
        }
        segt[i] += val;
        // cout<<"i = "<<i<<", segt size = "<<segt.size()<<endl;
        // cout<<"val = "<<segt[i]<<endl;
    }
    int sum(int a, int b, int i, int l, int r) {
        // cout<<"a = "<<a<<", b = "<<b<<", i = "<<i<<", l = "<<l<<", r = "<<r<<endl;
        if(l<=b && r>=a){
            //intersection
            // cout<<"Intersection"<<endl;
            if(a<=l && b>=r){
                //subset
                // cout<<"Subset"<<endl;
                return segt[i];
            }else{
                // cout<<"Partial Intersection"<<endl;
                return sum(a,b,2*i+1,l,(l+r)/2) + sum(a,b,2*i+2,1+(l+r)/2,r);
            }
        }else{
            // cout<<"Disjoint"<<endl;
            return 0;
        }
    }
public:
    Solution() {
        n = 2e4 + 1;
        segt = unordered_map<int,int>(2 * n - 1);
    }
    vector<int> countSmaller(vector<int>& nums) {
        vector<int> ans(nums.size());
        for(int i=nums.size()-1; i>=0; i--){
            update(nums[i]+1e4, 1);
            ans[i] = sum(0, nums[i]+1e4-1, 0, 0, n-1);
        }
        return ans;
    }
};
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