<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:

        def sink(nums, i, n):

            while 2 * i + 1 <= n - 1:

                j = 2 * i + 1

                if j < n - 1:
                    if nums[j] < nums[j + 1]:
                        j += 1
                if nums[i] > nums[j]:
                    break
                else:
                    temp = nums[i]
                    nums[i] = nums[j]
                    nums[j] = temp

                i = j

        def swim(nums, i):
            
            while i != 0:

                j = (k+1) // 2 -1

                if nums[i] > nums[j]:
                    break
                else:
                    temp = nums[i]
                    nums[i] = nums[j]
                    nums[j] = temp

                i = j

        n = len(nums)
        print(f"Total {n} Numbers")
        for i in range(n // 2 - 1, -1, -1):
            sink(nums, i, n)

        prev = None

        cancel = False

        set_nums = []
        cnt = []

        temp = []
        temp_cnt = {}

        for i in range(n - 1, -1, -1):

            if cancel:

                if len(temp) < k:
                    temp.append(prev - nums[0])
                    if len(temp) == k:
                        for i in range(k // 2 - 1, -1, -1):
                            sink(temp, i, k)
                else:
                    if prev - nums[0] < temp[0]:
                        temp[0] = prev - nums[0]
                        sink(temp, 0, k)

            if len(set_nums) == 0:
                set_nums.append(nums[0])
                cnt = [1]

            elif set_nums[0] == nums[0]:
                cnt[0] += 1
            else:
                if cancel:
                    diff = set_nums[0] - nums[0]

                    if diff not in temp_cnt:
                        temp.append(diff)
                        temp_cnt[diff] = 1
                    else:
                        temp_cnt[diff] += 1

                set_nums = [nums[0]] + set_nums
                cnt = [1] + cnt

            prev = nums[0]
            nums[0] = nums[i]
            nums[i] = prev
            sink(nums, 0, i)

        zeros = 0

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

        print(f"Total: {zeros} zeros")
        print(f"Set Num: {set_nums}")
        print(f"Set Cnt: {cnt}")
        print(f"Temp Num: {temp}")
        print(f"Temp Cnt: {temp_cnt}")
        if zeros >= k:
            return 0

        for j in range(len(temp) // 2 - 1, -1, -1):
            sink(temp, j, len(temp))

        max_diff = set_nums[-1] - set_nums[0]

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

        n = len(set_nums)
        # print(f'nums: {nums}')

        #n = min(50, len(set_nums))
        total_now = zeros


        for i in range(0, n - 1):
            for diff in range(1, n - i):

                # print(f'checking i: {i} | diff: {diff}')

                btw = set_nums[i + diff] - set_nums[i]
                # print(f'i: {i} - {i+diff} | {btw}')
                diff_cnt = cnt[i + diff] * cnt[i]

                if total_now < k:
                    
                    
                    temp_cnt[btw] += diff_cnt
                    total_now += diff_cnt
                    
                    curr_max = -1

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

                        print('---- Temp Full ----')
                        print(f'   temp: {temp}')
                        print(f' counts: {temp_cnt}')

                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(j, -1,-1):
                                if temp_cnt[j] != 0:
                                    curr_max = j
                                    break                        

                    else:
                        break
            # print(f' temp: {temp}')

        #print(f"temp: {temp}")
        print(f"Total {temp_cnt} searched")
        print(f"Total {max(temp_cnt)} max diff")
        return curr_max

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