<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:
    int kthSmallest(vector<vector<int>>& mat, int k) {
        priority_queue < pair<int,vector<int>>> pq;
        vector<int>curr(mat.size(),0);
        int val=0;
        for (int i=0;i<mat.size();i++) {
            val+=mat[i][0];
        } 
        pq.push({-val,curr});

        int cnt=0;
        set<vector<int>>visited;
        while (!pq.empty()) {
            int value=0-pq.top().first;
            vector<int>index=pq.top().second;
            vector<int>cpy=index;
            for (int i=0;i<index.size();i++) {
                cout<<index[i]<<" ";
            }
            cout<<value<<endl;
            int newy=value;
            pq.pop();

            if (visited.find(index)!=visited.end()) {
                continue;
            }
            visited.insert(index);

            cnt++;
            if (cnt==k) {
                return value;
            }

            for (int i=0;i<index.size();i++) {
                if (index[i]!=mat[0].size()-1) {
                    cpy[i]++;
                    newy+=mat[i][cpy[i]]-mat[i][index[i]];

                    pq.push({-newy,cpy});
                    cpy[i]--;
                    newy-=mat[i][cpy[i]+1]-mat[i][index[i]];

                }
            }
        }
        return 0;
    }
};
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