<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:
    vector<vector<int>> kSmallestPairs(vector<int>& nums1, vector<int>& nums2, int k) {
        // Two pointer approach
        // 1, 7
        // 2, 4
        int l = 0, r = 0;
        vector<vector<int>> ans;
        priority_queue<pair<int, vector<int>>, 
                   vector<pair<int, vector<int>>>, 
                   greater<pair<int, vector<int>>>> pq;
        set<pair<int, int>> visited;
        while(ans.size() < k) {
            if(pq.empty()) {
                ans.push_back({nums1[0], nums2[0]});
            }
            else {
                pair<int, vector<int>> tp = pq.top();
                vector<int> cur = tp.second;
                pq.pop();
                ans.push_back({nums1[cur[0]], nums2[cur[1]]});
                l = cur[0], r = cur[1];
            }
            // cout<<l<<" "<<r<<endl;
            if(l+1 < nums1.size() && visited.find({l+1, r}) == visited.end()) {
                visited.insert(make_pair(l+1, r));
                pq.push({nums1[l+1]+nums2[r], {l+1, r}});
            }
            if(r+1 < nums2.size() && visited.find({l, r+1}) == visited.end()) {
                visited.insert(make_pair(l, r+1));
                pq.push({nums1[l]+nums2[r+1], {l, r+1}});
            }
        }
    
        return ans;
    }
};
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