<p>Given an <code>m x n</code> matrix <code>matrix</code> and an integer <code>k</code>, return <em>the max sum of a rectangle in the matrix such that its sum is no larger than</em> <code>k</code>.</p>

<p>It is <strong>guaranteed</strong> that there will be a rectangle with a sum no larger than <code>k</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/18/sum-grid.jpg" style="width: 255px; height: 176px;" />
<pre>
<strong>Input:</strong> matrix = [[1,0,1],[0,-2,3]], k = 2
<strong>Output:</strong> 2
<strong>Explanation:</strong> Because the sum of the blue rectangle [[0, 1], [-2, 3]] is 2, and 2 is the max number no larger than k (k = 2).
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> matrix = [[2,2,-1]], k = 3
<strong>Output:</strong> 3
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 100</code></li>
	<li><code>-100 &lt;= matrix[i][j] &lt;= 100</code></li>
	<li><code>-10<sup>5</sup> &lt;= k &lt;= 10<sup>5</sup></code></li>
</ul>

<p>&nbsp;</p>
<p><strong>Follow up:</strong> What if the number of rows is much larger than the number of columns?</p>

class Solution {
public:
    int best_cumulative_sum(vector<int>ar,int K) 
{ 
    int N= ar.size();
    set<int> cumset; 
    cumset.insert(0); 
 
    int best=INT_MIN,cum=0; 
 
    for(int i=0;i<N;i++) 
    { 
        cum+=ar[i]; 
        set<int>::iterator sit=cumset.lower_bound(cum-K); 
        if(sit!=cumset.end())best=max(best,cum-*sit); 
        if(best==K) return best;
        cumset.insert(cum); 
    } 
    return best; 
} 
    int maxSumSubmatrix(vector<vector<int>>& matrix, int k) {
        int sum=INT_MIN;
        int m=matrix.size();
        int n= matrix[0].size();
        for(int j=0;j<n;j++){
            vector<int>prefix(m,0);
            for(int l=j;l<n;l++){
                for(int p=0;p<m;p++){
                    prefix[p]+=matrix[p][l];
                }
                sum=max(sum,best_cumulative_sum(prefix, k));
                if(sum==k) return k;
            }
        }
        return sum;
    }
};
87551