<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 kadanes(vector<int>& v,int k){
        int right=0,left,n=v.size(),ans=INT_MIN;
        set<int> st;
        st.insert(0);
        for(int i=0;i<n;i++){
            right+=v[i];
            auto it=lower_bound(st.begin(),st.end(),right-k);
            if(it!=st.end()){
                left=*it;
                ans=max(ans,right-left);
            }
            st.insert(right);
        }
        return ans;
    }
    int maxSumSubmatrix(vector<vector<int>>& matrix, int l) {
        int n=matrix.size();
        int m=matrix[0].size();
        int ans=INT_MIN;
        for(int i=0;i<n;i++){
            vector<int> v(m,0);
            for(int j=i;j<n;j++){

                for(int k=0;k<m;k++){
                    v[k]+=matrix[j][k];
                }
                int temp=kadanes(v,l);
                ans=max(ans,temp);
            }
        }
        return ans;
    }
};
192399