<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:
        value_count = {} # value: count
        count1 = [0] * (max(nums) - min(nums) + 1)

        for n in nums:
            if n not in value_count:
                value_count[n] = 0
            value_count[n] += 1

        seen = set()
        for value1 in value_count.keys():
            for value2 in value_count.keys():
                if value2 in seen:
                    continue
                if value1 != value2:
                    seen.add(value1)
                    count1[abs(value1 - value2)] += value_count[value1] * value_count[value2]
                else:
                    count1[0] += (value_count[value1] * (value_count[value1] - 1)) // 2

        # print(count1)

        # count = [0] * (max(nums) - min(nums) + 1)
        # for i in range(len(nums)):
        #     for j in range(i + 1, len(nums)):
        #         count[abs(nums[i] - nums[j])] += 1
        
        total = 0
        i = 0
        while total < k:
            total += count1[i]
            i += 1
        
        # print(count)

        return i - 1
25888