<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<vector<int>,vector<vector<int>>,greater<vector<int>>> pq;
        int currSum = 0;
        for(int i=0;i<mat.size();i++)
        {
            currSum += mat[i][0];
        }
        vector<int> key(mat.size()+1,0);
        map<vector<int>,int> vis;
        key[0] = currSum;
        vis[key] = 1;
        pq.push(key);
        while(--k)
        {
            auto ele = pq.top();
            pq.pop();
            for(int i=1;i<ele.size();i++)
            {
                vector<int> temp = ele;
                if(ele[i]+1>=mat[0].size()) continue;
                // cout << ele.size() << endl;
                // cout << i-1 << " " << ele[i]+1 << " " << endl;
                temp[0] += mat[i-1][ele[i]+1] - mat[i-1][ele[i]];
                temp[i] = ele[i] + 1;
                if(vis[temp]==0 && temp[i]<mat[0].size() && pq.size()<10000)
                {
                    pq.push(temp);
                    vis[temp] = 1;
                }
            }
        }
        return pq.top()[0];
    }
};
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