impl Solution {
    pub fn k_inverse_pairs(n: i32, k: i32) -> i32 {
        let MOD = 1000000007;

        let idx = |i, j| (i * (k + 1) + j) as usize;
        let get = |dp: &[i32], i: i32, j: i32| {
            if i < 0 || i > n || j < 0 || j > k {
                return 0;
            }

            dp[idx(i, j)]
        };

        let mut dp = vec![0; ((n + 1) * (k + 1)) as usize];
        for (i, j) in (1..=n).flat_map(|i| (0..=k).map(move |j| (i, j))) {
            if j == 0 {
                dp[idx(i, j)] = 1;
            } else {
                let val = (get(&dp, i - 1, j) + MOD - get(&dp, i - 1, j - i)) % MOD;
                dp[idx(i, j)] = (get(&dp, i, j - 1) + val) % MOD;
            }
        }

        (dp[idx(n, k)] + MOD - get(&dp, n, k - 1)) % MOD
    }
}