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)

use std::io::Write;

fn bfs(r: usize, g: &[Vec<usize>]) -> Vec<usize> {
    let n = g.len();
    let mut dp = vec![n; n];
    dp[r] = 0;
    let mut q = std::collections::VecDeque::new();
    q.push_back(r);
    while let Some(v) = q.pop_front() {
        for &u in g[v].iter() {
            if dp[u] > dp[v] + 1 {
                dp[u] = dp[v] + 1;
                q.push_back(u);
            }
        }
    }
    dp
}

fn run() {
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let n: usize = it.next().unwrap().parse().unwrap();
    let x: usize = it.next().unwrap().parse().unwrap();
    let y: usize = it.next().unwrap().parse().unwrap();
    let mut g = vec![vec![]; n];
    for i in 1..n {
        g[i - 1].push(i);
        g[i].push(i - 1);
    }
    g[x - 1].push(y - 1);
    g[y - 1].push(x - 1);
    let mut cnt = vec![0; n];
    for i in 0..n {
        let d = bfs(i, &g);
        for d in d.iter() {
            cnt[*d] += 1;
        }
    }
    for c in cnt.iter().skip(1) {
        let ans = *c / 2;
        writeln!(out, "{}", ans).ok();
    }
}

fn main() {
    run();
}