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)

macro_rules! scan_sub {
    ( $itr:ident, $t:ty ) => {
        let mut buf = String::new();
        let $itr = {
            while buf.trim().len() == 0 {
                buf = String::new();
                std::io::stdin().read_line(&mut buf).unwrap();
            }
            buf.split_whitespace().map(|n| n.parse::<$t>().unwrap())
        };
    };
}

macro_rules! scan {
    ( $x:ident; Vec<$t:ty> ) => {
        scan_sub!(itr, $t);
        let $x = itr.collect::<Vec<_>>();
    };
    ( $( $x:ident ),*; $t:ty ) => {
        scan_sub!(itr, $t);
        let mut itr = itr;
        $(
            let $x = itr.next().unwrap();
        )*
    };
}

/*
fn bfs(
    pre: usize, now: usize,
    graph: Vec<Vec<usize>>,
    res_array: mut Vec<usize>, used_book: mut HashMap<(usize, usize)>,
    visited: mut Vec<usize>, depth: usize
) {
    res_array[depth] += 1;
    visited[now] = true;

    for &i in graph[now].iter() {
        if not visited[i] {
            bfs(now, i, graph, book, visited, depth+1);
        }
    }
} */

use std::collections::HashMap;
use std::collections::VecDeque;

fn main() {
    scan!(n, x, y; usize);
    let x = x - 1;
    let y = y - 1;

    // グラフの構築
    let mut g = (0..n)
        .map(|_| Vec::with_capacity(3))
        .collect::<Vec<_>>();

    g[0].push(1);
    for i in 1..n-1 {
        g[i].push(i - 1);
        g[i].push(i + 1);
    }
    g[n-1].push(n - 2);

    g[x].push(y);
    g[y].push(x);

    // println!("{:?}", g);

    let mut res_array = vec![0; n];
    let mut used_book: HashMap<(usize, usize), bool> = HashMap::new();

    for i in 0..n {
        let mut visited = vec![false; n];
        visited[i] = true;

        let mut que: VecDeque<(usize, usize)> = VecDeque::new();

        g[i].iter().map(|&j| {
            que.push_front((j, 1));
        }).collect::<Vec<_>>();

        while let Some(node) = que.pop_back() {
            let (now, depth) = node;
            visited[now] = true;

            if used_book.get(&(i, now)).is_none() {
                res_array[depth] += 1;
                used_book.insert((i, now), true);
                used_book.insert((now, i), true);
            }

            for &j in g[now].iter() {
                if !visited[j] {
                    que.push_front((j, depth+1));
                }
            }
        }
    }

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