<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 Data
{
    int sum;
    vector<int> rowIndex;
    Data(int sumValue, const vector<int>& rowIdx)
    {
        sum = sumValue;
        rowIndex = rowIdx;
    }
};

class Comparator
{
   public:
      bool operator() (const Data& d1, const Data&d2)
      {
         return d1.sum > d2.sum;
      }
};

class Solution {
public:
    int kthSmallest(vector<vector<int>>& mat, int k) {
        int nRow = mat.size();
        int nCol = mat[0].size();
        int curSum = 0;

        for (int ii = 0; ii < nRow; ii++)
        {
            curSum += mat[ii][0];
        }
    
        priority_queue<Data, vector<Data>, Comparator> pq;
        pq.push(Data(curSum, vector<int>(nRow, 0)));
        int counter = 0;
        set<string> visited;
        string curIndexStr = "";
        for(int ii = 0; ii < nRow; ii++)
        {
           curIndexStr.append(to_string(0) + "_");
        }
        visited.insert(curIndexStr);

        while(counter < k)
        {
            Data data = pq.top();
            pq.pop();
            curSum = data.sum;
            vector<int> curRowIndex = data.rowIndex;
            for (int ii = 0; ii < nRow; ii++)
            {
               if (curRowIndex[ii] < nCol - 1)
               {
                  curRowIndex[ii]++;
                  curIndexStr = "";
                  for(int jj = 0; jj < nRow; jj++)
                  {
                     curIndexStr.append(to_string(curRowIndex[jj]) + "_");
                  }

                  if (visited.count(curIndexStr) == 0)
                  {
                    int newSum = curSum + mat[ii][curRowIndex[ii]] - mat[ii][curRowIndex[ii] - 1];
                    pq.push(Data(newSum, curRowIndex));
                    visited.insert(curIndexStr);
                  }
                  curRowIndex[ii]--;
               }
            }

            counter++;
        }

        return curSum;
    }
};
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