<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 {
public:    
    int smallestDistancePair(vector<int>& nums, int k) {
        // auto cmp = [](pair<int,int> a, pair<int,int> b) { 
        //     if (a.first < b.first) {
        //         return true;
        //     } else if (a.first > b.first) {
        //         return false;
        //     }
        //     return a.second < b.second;
        // };
        // priority_queue<pair<int,int>, vector<pair<int,int>>, decltype(cmp)> pq;
        // for (int i = 0; i < nums.size()-1; i++) {
        //     for (int j = i+1; j < nums.size(); j++) {
        //         int diff = abs(nums[i] - nums[j]);
        //         if (pq.size() < k) {
        //             pq.push(pair<int,int>(diff,i));
        //         } else if (pq.top().first > diff) {
        //             pq.pop();
        //             pq.push(pair<int,int>(diff,i));
        //         }
        //     }
        // }
        // return pq.top().first;
        vector<int> diffcount(1000001,0);
        int maxdiff = 0;
        for (int i = 0; i < nums.size(); i++) {
            for (int j = i+1; j < nums.size(); j++) {
                int diff = abs(nums[i]-nums[j]);
                if (diff > maxdiff) {
                    maxdiff = diff;
                }
                diffcount[diff] += 1;
            }
        }
        vector<int> presum(1000001,0);
        presum[0] = diffcount[0];
        for (int i = 1; i < maxdiff+1; i++) {
            presum[i] = presum[i-1] + diffcount[i];
        }
        int lo = 0;
        int hi = maxdiff;
        int mid = lo + (hi-lo)/2;
        // bool found = false;
        while (lo < hi) {
            // cout << "\nbefore lo=" << lo << ",hi=" << hi << ",mid=" << mid << ",count=" << presum[mid];
            if (presum[mid-1] < k && presum[mid] >= k) {
                break;
            }
            if (presum[mid] < k) {
                lo = mid+1;
                mid = lo + (hi-lo)/2;
            } else if (presum[mid] >= k) {
                hi = mid-1;
                mid = lo + (hi-lo)/2;
            }
            // cout << "\nafter lo=" << lo << ",hi=" << hi << ",mid=" << mid << ",count=" << presum[mid];
        }
        return mid;
    }
};

// diff 0 1 2 3 3 5 6
// dico 1 1 1 2 2 1 1
//      0 1 2 3 4 5 6 
// pre  1 2 3 5 5 6 7

// 0 7
//  3
141679