<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]:
        ans = [0] * len(nums)

        # first element is value, second is original index
        def counter(a, b):
            i, j = 0, 0
            res = 0

            while i < len(a) and j < len(b):
                while j < len(b) and a[i][0] > b[j][0]:
                    j += 1

                target_idx = a[i][1]
                ans[target_idx] += j
                i += 1

            while i < len(a):
                target_idx = a[i][1]
                ans[target_idx] += j
                i += 1

        def merge(l, r):
            if l == r:
                return [
                    (nums[l], l)
                ]

            m = (l + r)//2
            l_arr, r_arr = merge(l, m), merge(m + 1, r)

            counter(l_arr, r_arr)
            
            arr = [0] * (len(l_arr) + len(r_arr))
            i, j, k = 0, 0, 0
            while i < len(l_arr) and j < len(r_arr):
                if l_arr[i][0] <= r_arr[j][0]:
                    arr[k] = l_arr[i]
                    i += 1
                else:
                    arr[k] = r_arr[j]
                    j += 1

                k += 1

            # fill remaining
            while i < len(l_arr):
                arr[k] = l_arr[i]
                i += 1
                k += 1

            while j < len(r_arr):
                arr[k] = r_arr[j]
                j += 1
                k += 1
            
            return arr
        
        merge(0, len(nums) - 1)
        return ans

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