<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 {
    void findMax(vector<int> &temp, int k, int &ans){
        set<int> found={0};
        int i,n=temp.size(),x=0;
        for(i=0; i<n; i++){
            x+=temp[i];
            auto it=found.lower_bound(x-k);
            if(it!=found.end())
                ans=max(ans, x-*it);
            found.insert(x);
        }
    }
public:
    int maxSumSubmatrix(vector<vector<int>>& matrix, int k) {
        int m=matrix.size(),n=matrix[0].size(),i,j,c1,c2,r,ans=INT_MIN;
        for(c1=0; c1<n; c1++){
            vector<int> temp(m,0);
            for(c2=c1; c2<n; c2++){
                for(r=0; r<m; r++){
                    temp[r]+=matrix[r][c2];
                }
                findMax(temp, k, ans);
            }
        }
        return ans;
    }
};

/*
x-y<=k
y>=x-k, upper_bound
*/
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