<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 maxSumarray(vector<int>& A, int k){
        int sum = 0, res = INT_MIN;
        for(int a: A){
            sum += a;
            if(sum < a) sum = a;
            res = max(res, sum);
            if(res == k) return res;
        }
        // cout<< res << " @@ " << endl;
        if(res<=k) return res;
        
        set<int> st;
        st.insert(0);
        sum = 0, res = INT_MIN;
        for(int i=0;i<A.size();i++){
            sum += A[i];
            auto it = st.lower_bound(sum - k);
            if(it!=st.end()){
                res = max(res, sum - *it);
            }
            st.insert(sum);
        }
        // cout<< res << " @@@ " << endl;
        return res;
    }
    
    int maxSumSubmatrix(vector<vector<int>>& A, int k) {
        int m = A.size(), n = m>0 ? A[0].size(): 0;
        int res = INT_MIN;
        for(int c=0;c<n;c++){
            vector<int> arr(m, 0);
            for(int j=c;j<n;j++){
                for(int i=0;i<m;i++){
                    arr[i] += A[i][j];
                }
                
                /// now find the largest sum array having atmost sum k (contigiously)
                int ms = maxSumarray(arr, k);
                
                if(ms == k) return ms;
                if(ms<k && ms>res) res = ms;
            }
        }
        return res;
    }
};
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