<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>

struct node{
    int sum;
    vector<int> indexes;
    node(){
        this->sum = 0;
        this->indexes.clear();
    }
    node(int sum,vector<int> indexes){
        this->sum = sum;
        this->indexes = indexes;
    }
};

auto lambdaFunction = [](node &a, node &b){
    if(a.sum <= b.sum){
        return false;
    }
    else{
        return true;
    }
};

class Solution {
public:

    int getKthSmallest(vector<vector<int> > &mat,int k, priority_queue<node,vector<node>,decltype (lambdaFunction) > sums){
        int kSmallest,rows = mat.size(), cols = mat[0].size();
        set<vector<int> > isVisited;
        vector<int> dummy(rows,0); isVisited.insert(dummy);
        int iter = 1;
        while(k--){
            node currNode = sums.top(); sums.pop();
            // isVisited.insert(currNode.indexes);
            // cout<<iter<<".........\n";
            // cout<<currNode.sum<<"\n";
            // for(int i=0; i<rows; i++){
            //     cout<<currNode.indexes[i]<<" ";
            // }
            // cout<<"\n";
            if(!k){
                kSmallest = currNode.sum;
                break;
            }
            for(int i=0; i<rows; i++){
                if(currNode.indexes[i] != cols-1){
                    int nextSum = currNode.sum+mat[i][currNode.indexes[i]+1] - mat[i][currNode.indexes[i]];
                    vector<int> indexes = currNode.indexes;
                    indexes[i]++;
                    node newNode; newNode.sum = nextSum; newNode.indexes = indexes;
                    if(isVisited.find(indexes) == isVisited.end()){
                        sums.push(newNode);
                        isVisited.insert(indexes);
                    }  
                }
            }
            iter++;
        }

        return kSmallest;

    }

    int kthSmallest(vector<vector<int>>& mat, int k) {

        priority_queue<node,vector<node>,decltype (lambdaFunction) > sums;

        node leastSum; int minSum = 0;

        for(int i=0; i<mat.size(); i++){
            minSum += mat[i][0];
            leastSum.indexes.push_back(0);
        }

        leastSum.sum = minSum;

        sums.push(leastSum);

        return getKthSmallest(mat,k,sums);

    }
};
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