Problem:
Score : 400 points

Problem Statement

We have an undirected graph G with N vertices numbered 1 to N and N edges as follows:

For each i=1,2,...,N-1, there is an edge between Vertex i and Vertex i+1.

There is an edge between Vertex X and Vertex Y.

For each k=1,2,...,N-1, solve the problem below:

Find the number of pairs of integers (i,j) (1 \leq i < j \leq N) such that the shortest distance between Vertex i and Vertex j in G is k.

Constraints

3 \leq N \leq 2 \times 10^3

1 \leq X,Y \leq N

X+1 < Y

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N X Y

Output

For each k=1, 2, ..., N-1 in this order, print a line containing the answer to the problem.

Sample Input 1

5 2 4

Sample Output 1

5
4
1
0

The graph in this input is as follows:

There are five pairs (i,j) (1 \leq i < j \leq N) such that the shortest distance between Vertex i and Vertex j is 1: (1,2)\,,(2,3)\,,(2,4)\,,(3,4)\,,(4,5).

There are four pairs (i,j) (1 \leq i < j \leq N) such that the shortest distance between Vertex i and Vertex j is 2: (1,3)\,,(1,4)\,,(2,5)\,,(3,5).

There is one pair (i,j) (1 \leq i < j \leq N) such that the shortest distance between Vertex i and Vertex j is 3: (1,5).

There are no pairs (i,j) (1 \leq i < j \leq N) such that the shortest distance between Vertex i and Vertex j is 4.

Sample Input 2

3 1 3

Sample Output 2

3
0

The graph in this input is as follows:

Sample Input 3

7 3 7

Sample Output 3

7
8
4
2
0
0

Sample Input 4

10 4 8

Sample Output 4

10
12
10
8
4
1
0
0
0

Solution in Rust (1.15.1) (judge verdict: Accepted)

pub fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

use std::collections::BinaryHeap;

fn f(s: usize, n: usize, edges: &mut Vec<Vec<usize>>, cnt: &mut Vec<u32>) {
    let mut dis: Vec<usize> = vec![n; n];

    let mut bh: BinaryHeap<i32> = BinaryHeap::new();

    let tmp = 0 * 10000 + s as i32;
    bh.push(-tmp);

    while let Some(tmp) = bh.pop() {
        let tmp = (-tmp) as usize;
        let d = tmp / 10000;
        let u = tmp % 10000;
        if d < dis[u] {
            dis[u] = d;
        } else {
            continue;
        }
        for &v in &edges[u] {
            let tmp = ((d + 1) * 10000 + v) as i32;
            bh.push(-tmp);
        }
    }

    for i in 0..n {
        cnt[dis[i]] += 1;
    }
}

fn main() {
    let nxy: Vec<usize> = read_vec();
    let n = nxy[0];
    let x = nxy[1] - 1;
    let y = nxy[2] - 1;

    let mut edges: Vec<Vec<usize>> = vec![vec![]; n];

    for i in 0..n - 1 {
        edges[i].push(i + 1);
        edges[i + 1].push(i);
    }
    edges[x].push(y);
    edges[y].push(x);

    let mut cnt: Vec<u32> = vec![0; n];

    for i in 0..n {
        f(i, n, &mut edges, &mut cnt);
    }

    for i in 1..n {
        println!("{}", cnt[i] / 2);
    }
}