struct Solution;

impl Solution {
    fn matrix_block_sum(mat: Vec<Vec<i32>>, k: i32) -> Vec<Vec<i32>> {
        let n = mat.len();
        let m = mat[0].len();
        let mut prefix: Vec<Vec<i32>> = vec![vec![0; m]; n];
        let mut res: Vec<Vec<i32>> = vec![vec![0; m]; n];
        for i in 0..n {
            for j in 0..m {
                prefix[i][j] += mat[i][j];
                if i > 0 {
                    prefix[i][j] += prefix[i - 1][j];
                }
                if j > 0 {
                    prefix[i][j] += prefix[i][j - 1];
                }
                if i > 0 && j > 0 {
                    prefix[i][j] -= prefix[i - 1][j - 1];
                }
            }
        }
        for i in 0..n {
            for j in 0..m {
                let l = j as i32 - k;
                let r = j as i32 + k;
                let t = i as i32 - k;
                let b = i as i32 + k;
                let l = if l < 0 { 0 } else { l as usize };
                let r = if r >= m as i32 { m - 1 } else { r as usize };
                let t = if t < 0 { 0 } else { t as usize };
                let b = if b >= n as i32 { n - 1 } else { b as usize };
                res[i][j] = Self::sum(t, l, b, r, &prefix);
            }
        }
        res
    }

    fn sum(t: usize, l: usize, b: usize, r: usize, prefix: &[Vec<i32>]) -> i32 {
        let mut res = prefix[b][r];
        if l > 0 {
            res -= prefix[b][l - 1];
        }
        if t > 0 {
            res -= prefix[t - 1][r];
        }
        if l > 0 && t > 0 {
            res += prefix[t - 1][l - 1];
        }
        res
    }
}

#[test]
fn test() {
    let mat = vec_vec_i32![[1, 2, 3], [4, 5, 6], [7, 8, 9]];
    let k = 1;
    let res = vec_vec_i32![[12, 21, 16], [27, 45, 33], [24, 39, 28]];
    assert_eq!(Solution::matrix_block_sum(mat, k), res);
    let mat = vec_vec_i32![[1, 2, 3], [4, 5, 6], [7, 8, 9]];
    let k = 2;
    let res = vec_vec_i32![[45, 45, 45], [45, 45, 45], [45, 45, 45]];
    assert_eq!(Solution::matrix_block_sum(mat, k), res);
}