<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 binary_search_helper(self, num, start, end):
        mid = (start + end) // 2
        
        if self.sorted[mid - 1] < num <= self.sorted[mid]:
            self.sorted.insert(mid, num)
            return mid
        elif self.sorted[mid] < num <= self.sorted[mid + 1]:
            self.sorted.insert(mid + 1, num)
            return mid + 1
        elif self.sorted[mid] >= num:
            return self.binary_search_helper(num, start, mid - 1)
        else:
            return self.binary_search_helper(num, mid + 1, end)
    
    def binary_search(self, num: int) -> int:
        if len(self.sorted) == 0:
            self.sorted.append(num)
            return 0
        elif self.sorted[len(self.sorted) - 1] < num:
            self.sorted.append(num)
            return len(self.sorted) - 1
        elif self.sorted[0] >= num:
            self.sorted.insert(0, num)
            return 0
        else:
            return self.binary_search_helper(num, 0, len(self.sorted))
    
    def countSmaller(self, nums: List[int]) -> List[int]:
        res = []
        self.sorted = []
        
        for num in nums[::-1]:
            res.append(self.binary_search(num))
        
        return res[::-1]
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