<p>You have <code>k</code> lists of sorted integers in <strong>non-decreasing&nbsp;order</strong>. Find the <b>smallest</b> range that includes at least one number from each of the <code>k</code> lists.</p>

<p>We define the range <code>[a, b]</code> is smaller than range <code>[c, d]</code> if <code>b - a &lt; d - c</code> <strong>or</strong> <code>a &lt; c</code> if <code>b - a == d - c</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [[4,10,15,24,26],[0,9,12,20],[5,18,22,30]]
<strong>Output:</strong> [20,24]
<strong>Explanation: </strong>
List 1: [4, 10, 15, 24,26], 24 is in range [20,24].
List 2: [0, 9, 12, 20], 20 is in range [20,24].
List 3: [5, 18, 22, 30], 22 is in range [20,24].
</pre>

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

<pre>
<strong>Input:</strong> nums = [[1,2,3],[1,2,3],[1,2,3]]
<strong>Output:</strong> [1,1]
</pre>

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

<ul>
	<li><code>nums.length == k</code></li>
	<li><code>1 &lt;= k &lt;= 3500</code></li>
	<li><code>1 &lt;= nums[i].length &lt;= 50</code></li>
	<li><code>-10<sup>5</sup> &lt;= nums[i][j] &lt;= 10<sup>5</sup></code></li>
	<li><code>nums[i]</code>&nbsp;is sorted in <strong>non-decreasing</strong> order.</li>
</ul>

class Solution {
public:
    auto mergeToListIndex(const std::vector<vector<int>>& nums){
        using CompFunction = std::function<bool(std::pair<int, int>, std::pair<int, int>)>;
        const auto comp = [&](auto a, auto b){
            const auto [indexA, listIndexA] = a;
            const auto [indexB, listIndexB] = b;

            return nums[listIndexA][indexA] > nums[listIndexB][indexB];
        };

        std::priority_queue<std::pair<int, int>, std::vector<std::pair<int, int>>, CompFunction> pq(comp);

        for(std::size_t i = 0; i < nums.size(); i++){
            pq.push({0, i});
        }

        std::vector<std::pair<std::size_t, std::size_t>> sortedNums;

        while(!pq.empty()){
            const auto [index, listIndex] = pq.top();
            pq.pop();

            sortedNums.push_back({index, listIndex});
            if(index != nums[listIndex].size() - 1){
                pq.push({index+1, listIndex});
            }
        }

        return sortedNums;
    }

    vector<int> smallestRange(vector<vector<int>>& nums) {
        const auto sortedNums = mergeToListIndex(nums);

        std::vector<int> sol = {0, std::numeric_limits<int>::max()};
        int seenCount = 0;
        std::vector<int> count(nums.size(), 0);

        std::size_t l = 0;
        for(std::size_t r = 0; r < sortedNums.size(); r++){
            const auto [indexR, listIndexR] = sortedNums[r];
            count[listIndexR]++;
            if(count[listIndexR] == 1){
                seenCount++;
            }

            if(seenCount == nums.size()){
                while(count[sortedNums[l].second] > 1){
                    count[sortedNums[l].second]--;
                    l++;
                }

                if(nums[listIndexR][indexR] - nums[sortedNums[l].second][sortedNums[l].first] < sol[1]-sol[0]){
                    sol = {nums[sortedNums[l].second][sortedNums[l].first], nums[listIndexR][indexR]};
                }
            }
        }

        return sol;
    }
};
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