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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#![allow(unused_imports)]
use itertools::Itertools;
use proconio::input;
use std::cmp::*;
use std::collections::*;
use superslice::*;
fn main() {
    input! {
        n: usize, x: usize, y: usize,
    }
    let x = x - 1;
    let y = y - 1;

    let mut nodes = vec![Vec::new(); n];
    for i in 0..n {
        if i == 0 {
            nodes[i].push(1);
        } else if i == n - 1 {
            nodes[i].push(n-2);
        } else {
            nodes[i].push(i-1);
            nodes[i].push(i+1);
        }
        if i == x {
            nodes[i].push(y);
        } else if i == y {
            nodes[i].push(x);
        }
    }
    eprintln!("{:?}", nodes);
    let mut counts = vec![0; n];
    for i in 0..n {
        let mut dists = vec![0; n];
        let mut dets = vec![false; n];
        dets[i] = true;
        let mut q = VecDeque::new();
        q.push_back((i, 1));

        while let Some((now, dist)) = q.pop_front() {
            for &next in &nodes[now] {
                if dets[next] {
                    continue;
                }

                dists[next] = dist;
                dets[next] = true;
                q.push_back((next, dist+1));
            }
        }
        for dist in dists {
            counts[dist] += 1;
        }
    }

    for k in 1..=n-1 {
        println!("{}", counts[k] / 2);
    }
}
*/

fn main() {
    let exe = "/tmp/binAF7CBFC2";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";