LeetCode 363. Max Sum of Rectangle No Larger Than K

class Solution {
public:
    int maxSumSubmatrix(vector<vector<int>>& matrix, int k) {
        const int m = matrix.size(), n = matrix[0].size();
        int ans = INT_MIN;
        for (int i = 0; i < m; ++i) { // enumerate upper bound.
            vector<int> sum(n);
            for (int j = i; j < m; ++j) { // enumerate lower bound.
                for (int c = 0; c < n; ++c)
                    sum[c] += matrix[j][c]; // area sum of each column.
                // find the largest value that is
                // 1. smaller than k,
                // 2. from a continue subarray of `sum`.
                set<int> sumSet{0};
                int s = 0;
                for (int v : sum) {
                    s += v;
                    auto it = sumSet.lower_bound(s - k);
                    if (it != sumSet.end())
                        ans = max(ans, s - *it);
                    sumSet.insert(s);
                }
            }
        }
        return ans;
    }
};