<p>You are given two integer arrays <code>nums1</code> and <code>nums2</code> sorted in <strong>non-decreasing&nbsp;order</strong> and an integer <code>k</code>.</p>

<p>Define a pair <code>(u, v)</code> which consists of one element from the first array and one element from the second array.</p>

<p>Return <em>the</em> <code>k</code> <em>pairs</em> <code>(u<sub>1</sub>, v<sub>1</sub>), (u<sub>2</sub>, v<sub>2</sub>), ..., (u<sub>k</sub>, v<sub>k</sub>)</code> <em>with the smallest sums</em>.</p>

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

<pre>
<strong>Input:</strong> nums1 = [1,7,11], nums2 = [2,4,6], k = 3
<strong>Output:</strong> [[1,2],[1,4],[1,6]]
<strong>Explanation:</strong> The first 3 pairs are returned from the sequence: [1,2],[1,4],[1,6],[7,2],[7,4],[11,2],[7,6],[11,4],[11,6]
</pre>

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

<pre>
<strong>Input:</strong> nums1 = [1,1,2], nums2 = [1,2,3], k = 2
<strong>Output:</strong> [[1,1],[1,1]]
<strong>Explanation:</strong> The first 2 pairs are returned from the sequence: [1,1],[1,1],[1,2],[2,1],[1,2],[2,2],[1,3],[1,3],[2,3]
</pre>

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

<ul>
	<li><code>1 &lt;= nums1.length, nums2.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>9</sup> &lt;= nums1[i], nums2[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>nums1</code> and <code>nums2</code> both are sorted in <strong>non-decreasing order</strong>.</li>
	<li><code>1 &lt;= k &lt;= 10<sup>4</sup></code></li>
	<li><code>k &lt;=&nbsp;nums1.length *&nbsp;nums2.length</code></li>
</ul>

class Solution {
    struct Item {
        int ss{std::numeric_limits<int>::max()};

        std::uint16_t i{0};
        std::uint16_t j{0};

        constexpr auto operator<=>(const Item& other) const {
            return other.ss <=> ss;
        }
    };

public:
    std::vector<std::vector<int>> kSmallestPairs(const std::vector<int>& nums1,
                                                 const std::vector<int>& nums2,
                                                 const int k) {
        const int N1 = nums1.size();
        const int N2 = nums2.size();

        std::vector<std::vector<int>> out(k);
        int idx = 0;

        // std::unordered_set<int> visited;
        std::priority_queue<Item> Q;

        Q.emplace(nums1[0] + nums1[0], 0, 0);
        // visited.emplace(0);

        while (idx < k) {
            auto top = Q.top();
            Q.pop();
            out[idx++] = {nums1[top.i], nums2[top.j]};

            if (top.i + 1 < N1) {
                const int ni = top.i + 1;
                const int nj = top.j;
                
                Q.emplace(nums1[ni] + nums2[nj], ni, nj);
            }

            // The 0 constraint here, makes sure we are only getting unique combinations,
            // without having a visited table. Very clever.
            if (top.i == 0 && (top.j + 1 < N2)) {
                const int ni = top.i;
                const int nj = top.j + 1;
                Q.emplace(nums1[ni] + nums2[nj], ni, nj);
            }
        }

        return out;
    }
};
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