<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 {
    vector<vector<int>> minheap;

public:
    vector<vector<int>> kSmallestPairs(vector<int>& nums1, vector<int>& nums2,
                                       int k) {
        vector<vector<int>> ans;
        const int m = nums1.size();
        const int n = nums2.size();
        priority_queue<int,vector<int>,greater<int>> minheap;
        unordered_map<int,vector<vector<int>>> mymap;
        vector<unordered_set<int>> myset(m);
        
        minheap.push(nums1[0] + nums2[0]);
        mymap[nums1[0] + nums2[0]].push_back(vector<int>{0,0});

        for (int j = 0; j < k; j++) {
            int i = minheap.top();
            auto it = mymap.find(i);
            if(it == mymap.end()) return ans; // emergency breakout, if mymap is empty
            ans.push_back(vector<int>{nums1[it -> second[0][0]],nums2[it -> second[0][1]]});
            minheap.pop();

            int indexone = it -> second[0][0];
            int indextwo = it -> second[0][1];
            it -> second.erase(it -> second.begin());
            
            if (indexone + 1 < m && myset[indexone+1].find(indextwo) == myset[indexone+1].end()) {
                int sum = nums1[indexone+1] + nums2[indextwo];
                minheap.push(sum);
                mymap[sum].push_back(vector<int>{indexone+1,indextwo});
                myset[indexone+1].insert(indextwo);
            }
            if (indextwo + 1 < n && myset[indexone].find(indextwo+1) == myset[indexone].end()) {
                int sum = nums1[indexone] + nums2[indextwo+1];
                minheap.push(sum);
                mymap[sum].push_back(vector<int>{indexone,indextwo+1});
                myset[indexone].insert(indextwo+1);
            }
        }
        return ans;
    }
};
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