<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) {
        // pair<int,vector<int>> 
        int n  = mat.size();
        int m = mat[0].size();
        priority_queue<pair<int,vector<int>>,vector<pair<int,vector<int>>>,greater<pair<int,vector<int>>>> pq;
        vector<int> cur(n,0);
        set<vector<int>> vis;
        vis.insert(cur);
        int sum = 0;
        for(int i = 0;i<n;i++){
            sum+=mat[i][0];
        }

        pq.push({sum,cur});

        int ans;
        while(k--){
            auto [cur,order] = pq.top();
            pq.pop();
            ans = cur;
            // cout<<ans<<endl;
            
            for(int i = 0;i<n;i++){
                vector<int> copy = order;
                if(copy[i]+1<m){
                    // copy[i]++;
                    int temp = cur;
                    temp-=mat[i][copy[i]];
                    copy[i]++;
                    temp+=mat[i][copy[i]];
                    
                    if(vis.find(copy)==vis.end()){
                        pq.push({temp,copy});
                        vis.insert(copy);
                    }
                    
                }
            }
        }
        return ans;
    }
};
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