<p>The <strong>distance of a pair</strong> of integers <code>a</code> and <code>b</code> is defined as the absolute difference between <code>a</code> and <code>b</code>.</p>

<p>Given an integer array <code>nums</code> and an integer <code>k</code>, return <em>the</em> <code>k<sup>th</sup></code> <em>smallest <strong>distance among all the pairs</strong></em> <code>nums[i]</code> <em>and</em> <code>nums[j]</code> <em>where</em> <code>0 &lt;= i &lt; j &lt; nums.length</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,3,1], k = 1
<strong>Output:</strong> 0
<strong>Explanation:</strong> Here are all the pairs:
(1,3) -&gt; 2
(1,1) -&gt; 0
(3,1) -&gt; 2
Then the 1<sup>st</sup> smallest distance pair is (1,1), and its distance is 0.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,1], k = 2
<strong>Output:</strong> 0
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,6,1], k = 3
<strong>Output:</strong> 5
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == nums.length</code></li>
	<li><code>2 &lt;= n &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
	<li><code>1 &lt;= k &lt;= n * (n - 1) / 2</code></li>
</ul>

class Solution:
    def smallestDistancePair(self, nums: List[int], k: int) -> int:


        nums.sort()
        set_nums = list(set(nums))
        set_nums.sort()
        cnt = [0 for _ in range(len(set_nums))]
        j = 0
        for i in range(len(nums)):
            if nums[i] != set_nums[j]:
                j += 1
            cnt[j] += 1

        zeros = 0

        for i in cnt:
            if i > 1:
                zeros += int(i * (i - 1) / 2)

        if zeros >= k:
            return 0

        temp_cnt = [0 for _ in range(set_nums[-1]-set_nums[0]+1)]

        n = len(set_nums)

        total_now = zeros

        curr_max = float('-inf')
        for i in range(0, n - 1):
            for diff in range(1, n - i):

                btw = set_nums[i + diff] - set_nums[i]
                diff_cnt = cnt[i + diff] * cnt[i]

                if total_now < k:
         
                    temp_cnt[btw] += diff_cnt
                    total_now += diff_cnt
                    curr_max = max(curr_max, btw)

                else:
                    if btw < curr_max:
                                                
                        temp_cnt[btw] += diff_cnt
                        total_now += diff_cnt

                        if total_now - temp_cnt[curr_max] >= k:
                            
                            total_now -= temp_cnt[curr_max]
                            temp_cnt[curr_max] = 0
                            for j in range(curr_max, -1,-1):
                                if temp_cnt[j] != 0:
                                    curr_max = j
                                    break                        

                    else:
                        break
   
        return curr_max

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