<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 {
public:
    class Comp {
        public:
        bool operator()(const vector<int> &a, const vector<int> &b) const {
            if (a[0] == b[0]) {
                return a[1] < b[1];
            }
            return a[0] < b[0];
        }
    };

    class PComp {
        public:
        bool operator()(const vector<int> &a, const vector<int> &b) {
            return a[0] > b[0];
        }
    };

    vector<vector<int>> kSmallestPairs(vector<int>& nums1, vector<int>& nums2, int k) {
        set<vector<int>, Comp> visited;
        priority_queue<vector<int>, vector<vector<int>>, PComp> pq;
        vector<vector<int>> result;

        pq.push({nums1[0] + nums2[0], 0, 0});
        visited.insert({0, 0});

        while ((int)result.size() < k && !pq.empty()) {
            vector<int> curr = pq.top();
            pq.pop();
            int i = curr[1], j = curr[2];
            result.push_back({nums1[i], nums2[j]});
            vector<int> ip1 = {i + 1, j}, ip2 = {i, j + 1};
            if (i + 1 < (int)nums1.size() && visited.find(ip1) == visited.end()) {
                pq.push({nums1[i + 1] + nums2[j], i + 1, j});
                visited.insert(ip1);
            }
            if (j + 1 < (int)nums2.size() && visited.find(ip2) == visited.end()) {
                pq.push({nums1[i] + nums2[j + 1], i, j + 1});
                visited.insert(ip2);
            }
        }
        return result;
    }
};


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