<p>You are given an <code>m x n</code> matrix <code>mat</code> that has its rows sorted in non-decreasing order and an integer <code>k</code>.</p>

<p>You are allowed to choose <strong>exactly one element</strong> from each row to form an array.</p>

<p>Return <em>the </em><code>k<sup>th</sup></code><em> smallest array sum among all possible arrays</em>.</p>

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

<pre>
<strong>Input:</strong> mat = [[1,3,11],[2,4,6]], k = 5
<strong>Output:</strong> 7
<strong>Explanation:</strong> Choosing one element from each row, the first k smallest sum are:
[1,2], [1,4], [3,2], [3,4], [1,6]. Where the 5th sum is 7.
</pre>

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

<pre>
<strong>Input:</strong> mat = [[1,3,11],[2,4,6]], k = 9
<strong>Output:</strong> 17
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> mat = [[1,10,10],[1,4,5],[2,3,6]], k = 7
<strong>Output:</strong> 9
<strong>Explanation:</strong> Choosing one element from each row, the first k smallest sum are:
[1,1,2], [1,1,3], [1,4,2], [1,4,3], [1,1,6], [1,5,2], [1,5,3]. Where the 7th sum is 9.  
</pre>

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

<ul>
	<li><code>m == mat.length</code></li>
	<li><code>n == mat.length[i]</code></li>
	<li><code>1 &lt;= m, n &lt;= 40</code></li>
	<li><code>1 &lt;= mat[i][j] &lt;= 5000</code></li>
	<li><code>1 &lt;= k &lt;= min(200, n<sup>m</sup>)</code></li>
	<li><code>mat[i]</code> is a non-decreasing array.</li>
</ul>

class Solution {
public:
struct comparator{
    bool operator()(pair<int,vector<int>> a, pair<int,vector<int>> b){
        return a.first>b.first;
    }
};
    int kthSmallest(vector<vector<int>>& mat, int k) {
        int sum=0;
        priority_queue<pair<int,vector<int>>,vector<pair<int,vector<int>>>,comparator>pq;
        set<vector<int>>visited;
        vector<int>v(mat.size(),0);
        for(int i=0;i<mat.size();i++){
            sum+=mat[i][0];
        }

        pq.push({sum,v});
        visited.insert(v);
        int cnt=1;
        while(cnt!=k){
            cnt++;
            pair<int,vector<int>> top=pq.top();
            pq.pop();
            vector<int>vec=top.second;
            int sum=top.first;
            for(int i=0;i<vec.size();i++){
                if(vec[i]+1==mat[0].size())
                continue;
                int curr = sum-mat[i][vec[i]]+mat[i][vec[i]+1];
                
     
                vec[i]=vec[i]+1;
                cout<<curr<<endl;
                // for(int l=0;l<vec.size();l++)
                // cout<<vec[l]<<" ";
                // cout<<endl;
                if(visited.find(vec)==visited.end()){
                    visited.insert(vec);
                    pq.push({curr,vec});
                }
                vec[i]=vec[i]-1;
            }

        }
        return pq.top().first;
    }
};
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