<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:
    void disp(vector<int> &vec){
        for(auto i:vec) cout<<i<<" ";
        cout<<endl;
    }
    int kthSmallest(vector<vector<int>>& mat, int k) {
        int m = mat.size();
        vector<int> ind(m + 1,0);
        int n = mat[0].size();
        // priority_queue<vector<int>, vector<vector<int>>, greater<vector<int>>> q;
        set<vector<int>> q;
        for(int i = 0;i<m;i++){
            ind[0] += mat[i][0];
        }
        q.insert(ind);
        int cnt = 0;
        while(q.size()){
            // auto it = q.top();
            auto ptr = q.begin();
            vector<int> it = *(ptr);
            q.erase(ptr);
            cnt++;
            if(cnt==k) return it[0];
            cout<<"helo : "<<endl;
            disp(it);
            for(int i = 0;i<m;i++){
                int sum = it[0];
                int id = it[i+1];
                if(id<n-1){
                    sum -= mat[i][id];
                    sum += mat[i][id+1];
                    vector<int> temp = it;
                    temp[0] = sum;
                    temp[i+1]++;
                    // cout<<"helo : "<<<<endl;
                    q.insert(temp);
                }
            }
        }
        return 0;

    }
};
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