<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 Node{
public:
    shared_ptr<Node> left, right;
    int l, r, count; //count stores number of entries to the left
    Node(int l, int r) : l(l), r(r), count(0) {};
};
class Solution {
    shared_ptr<Node> root;
    void add(int k, shared_ptr<Node> cur_node) {
       int l = cur_node->l, r = cur_node->r;
       if(l == r) {
            cur_node->count += 1;
            return;
       }
       int m = l + (r - l)/ 2;
       if(k <= m) {
            if(cur_node->left == nullptr) {
                cur_node->left = make_shared<Node>(l, m);
            }
            add(k, cur_node->left);
       } else {
            if(cur_node->right == nullptr) {
                cur_node->right = make_shared<Node>(m+1, r);
            }
            add(k, cur_node->right);
       }
       cur_node->count = ((cur_node->left == nullptr) ? 0 : cur_node->left->count) + ((cur_node->right == nullptr) ? 0 : cur_node->right->count);
    }
    int count(int l, int r, shared_ptr<Node> cur_ptr) {
        if(cur_ptr == nullptr) {
            return 0;
        }
        if(r < cur_ptr->l || l > cur_ptr->r) {
            return 0;
        }
        if(l <= cur_ptr->l && cur_ptr->r <= r) {
            return cur_ptr->count;
        }
        return count(l, r, cur_ptr->left) + count(l, r, cur_ptr->right);
    }
public:
    vector<int> countSmaller(vector<int>& nums) {
        root = make_shared<Node>(-10000000, 10000000);
        vector<int> ans;
        for(auto it = nums.rbegin(); it != nums.rend(); ++it) {
            ans.push_back(count(-10000000,(*it)-1, root));
            // cout << "inserting " << *it << endl;
            add((*it), root);
        }
        reverse(ans.begin(), ans.end());
        return ans;
    }
};
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