<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 ds{
    //     int dif,int j,int i;
    // };
    class compare
    {
        public:
        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 n=mat.size();
        int m=mat[0].size();
        vector<int> temp(n);
        priority_queue<pair<int,vector<int>>,vector<pair<int,vector<int>>>,compare> pq;
        long long s=0;
        for(int i=0;i<n;i++)
        {
            s+=mat[i][0];
            temp[i]=0;
        }
        cout<<s<<endl;
        pq.push({s,temp});
        long long ans=s;
        // k++;
        int cnt=0;
        // if(k==cnt)
        // return s;
        set<vector<int>> vis;
        vis.insert(temp);
        while(!pq.empty())
        {
            auto it=pq.top();
            pq.pop();
            cnt++;
            if(cnt==k)
            return it.first;
            ans=it.first;
            s=it.first;
            vector<int> vec=it.second;
            for(int i=0;i<n;i++)
            {
                
                if(vec[i]==m-1)
                continue;

                vec[i]=vec[i]+1;
                long long t=s;
                t=t-mat[i][vec[i]-1]+mat[i][vec[i]];
                cout<<cnt<<" "<<s<<" "<<t<<endl;
                if(vis.find(vec)==vis.end()){
                pq.push({t,vec});
                vis.insert(vec);
                }
                vec[i]--;

            }
        }
        return ans;

    }
};
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