<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>

#define HEAPMEMBER pair<int,vector<int>>

class Solution {
public:

    set<vector<int>> us;

    void displayMinHeap(priority_queue<HEAPMEMBER, vector<HEAPMEMBER>, greater<HEAPMEMBER>> minh) {

        cout<<"Members of Heap : \n";
        while(!minh.empty())
        {
            int sum = minh.top().first;
            vector<int> itr = minh.top().second;
            minh.pop();

            cout<<"Sum : "<<sum<<" Iteration : ";
            for(auto &x : itr)
                cout<<x<<" ";
            cout<<"\n";
        }

    }


    vector<vector<int>> getNextMIteration(vector<int> &indices, int n) {
        vector<vector<int>> ans;
        int m = indices.size();

        for(int i = 0; i < m; i++)
        {
            if(indices[i] + 1 >= n)
            continue;
            indices[i]++;
            if(us.find(indices) == us.end())
            {
                ans.push_back(indices);
                us.insert(indices);
            }
            indices[i]--;
        }


        return ans;
    }

    long long getSum(vector<vector<int>>& mat, vector<int> &indices) {
        long long ans = 0;
        int m = mat.size();
        
        for(int i = 0; i < m; i++)
        ans += mat[i][indices[i]];

        return ans;
    }


    int kthSmallest(vector<vector<int>>& mat, int k) {
        int m = mat.size();
        int n = mat[0].size();
        vector<int> indices(m,0);
        int ans = INT_MAX;
        priority_queue<HEAPMEMBER, vector<HEAPMEMBER>, greater<HEAPMEMBER>> minh; 

        minh.push({getSum(mat,indices), indices});
        us.insert(indices);

        while(k--)
        {
            //displayMinHeap(minh);
            ans = minh.top().first;
            indices = minh.top().second;
            minh.pop();
            for(auto &x : getNextMIteration(indices,n))
                minh.push({getSum(mat,x), x});          
        }

        return ans;
    }
};
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