<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:

    int check(vector<vector<int>>& mat, int index, int currval, int value, int k)
    {
        int n = mat.size();
        int m = mat[0].size();

        if(index == n)
        {
            if(currval <= value) return 1;
            return 0;
        }
        int x = 0;
        for(int j=0;j<m;j++)
        {
            // if(currval + mat[index][j] > value) break;
            int ch = check(mat, index+1, currval+mat[index][j], value, k);

            if(ch == 0) return x;
            x+=ch;
            if(x > k) break;
        }
        // cout<<index<<' '<<currval<<' '<<value<<' '<<x<<endl;
        return x;
    }
    int kthSmallest(vector<vector<int>>& mat, int k) {
        int n = mat.size();
        int m = mat[0].size();
        int ans = -1;
        int l = 0, r = 1000000007;
        while(l<=r)
        {
            int mid = (l+r)/2;
            int ch = check(mat, 0, 0, mid, k);
            // cout<<mid<<' '<<ch<<endl;
            if(ch < k)
            {
               
                l = mid+1;
            }
            else {
                ans = mid;
                r = mid-1;
            }
        }
        return ans;
    }
};
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