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)

//  ____            _                  _                       _       _
// |  _ \ _   _ ___| |_    ___ _ __   | |_ ___ _ __ ___  _ __ | | __ _| |_ ___
// | |_) | | | / __| __|  / __| '_ \  | __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \
// |  _ <| |_| \__ \ |_  | (__| |_) | | ||  __/ | | | | | |_) | | (_| | ||  __/
// |_| \_\\__,_|___/\__|  \___| .__/___\__\___|_| |_| |_| .__/|_|\__,_|\__\___|
//                            |_| |_____|               |_|

//https://github.com/manta1130/Competitive_Programming_Template_Rust

#[macro_use]
mod input {

    use std;
    use std::io;

    const SPLIT_DELIMITER: char = ' ';

    #[macro_export]
    #[allow(unused_macros)]
    macro_rules! input {
    ( $($x:expr ),*) => {
        {
            let temp_str = input_line_str();
            let mut split_result_iter = temp_str.split_whitespace();
                $(
                let buf_split_result = split_result_iter.next();
                let buf_split_result = buf_split_result.unwrap();
                    ($x) = buf_split_result.parse().unwrap();
                )*
        }
    };
}

    #[allow(dead_code)]
    pub fn input_line_str() -> String {
        let mut s = String::new();
        io::stdin().read_line(&mut s).unwrap();
        s.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn p<T>(t: T)
    where
        T: std::fmt::Display,
    {
        println!("{}", t);
    }

    #[allow(dead_code)]
    pub fn input_vector2d<T>(line: usize) -> Vec<Vec<T>>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<Vec<T>> = Vec::new();

        for _ in 0..line {
            let vec_line = input_vector();
            v.push(vec_line);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector<T>() -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<T> = Vec::new();

        let s = input_line_str();
        let split_result = s.split(SPLIT_DELIMITER);
        for z in split_result {
            let buf = match z.parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector_row<T>(n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::with_capacity(n);
        for _ in 0..n {
            let buf = match input_line_str().parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    pub trait ToCharVec {
        fn to_charvec(&self) -> Vec<char>;
    }

    impl ToCharVec for String {
        fn to_charvec(&self) -> Vec<char> {
            self.to_string().chars().collect::<Vec<_>>()
        }
    }
}

mod graph {

use std;
use std::cmp;
use std::collections::BinaryHeap;

///最短経路計算(ベルマンフォード法)
///
///戻り値がtrueなら負の閉路がある。
///
///graph:グラフ情報(隣接リスト)
///
///dist:最短経路を格納する配列
///
///事前に始点には0を入れ、その他はNoneで初期化する必要がある。
pub fn bellman_ford(graph: &Vec<Vec<(usize, isize)>>, dist: &mut Vec<Option<isize>>) -> Vec<bool> {
    //負の閉路検出用
    let mut neg_flag = vec![false; dist.len()];

    for _ in 0..graph.len() {
        for (from, v) in graph.iter().enumerate() {
            for e in v {
                let cost = e.1;
                let to = e.0;
                if let Some(x) = dist[from] {
                    if let None = dist[to] {
                        dist[to] = Some(x + cost);
                    } else if let Some(y) = dist[to] {
                        if y > x + cost {
                            dist[to] = Some(x + cost);
                        }
                    }
                }
            }
        }
    }

    for _ in 0..graph.len() {
        for (from, v) in graph.iter().enumerate() {
            for e in v {
                let cost = e.1;
                let to = e.0;
                if let Some(x) = dist[from] {
                    if let None = dist[to] {
                        dist[to] = Some(x + cost);
                        neg_flag[to] = true;
                    } else if let Some(y) = dist[to] {
                        if y > x + cost {
                            dist[to] = Some(x + cost);
                            neg_flag[to] = true;
                        }
                    }
                }
                if neg_flag[from] {
                    neg_flag[to] = true;
                }
            }
        }
    }
    neg_flag
}

///最短経路計算(ダイクストラ法)
///
///最短経路が格納された配列を返す。(到達できない場合はisize::max_value()を返す。)
///
///graph:グラフ情報(隣接リスト)
///
///start:始点

pub fn dijkstra(graph: &Vec<Vec<(usize, isize)>>, start: usize) -> Vec<isize> {
    let mut heap = BinaryHeap::new();
    let mut dist = vec![isize::max_value(); graph.len()];
    dist[start] = 0;

    heap.push((0, start));

    while !heap.is_empty() {
        let e = heap.pop().unwrap();
        if -1 * e.0 > dist[e.1] {
            continue;
        }
        for next_e in &graph[e.1] {
            if dist[next_e.0] > next_e.1 + dist[e.1] {
                dist[next_e.0] = next_e.1 + dist[e.1];
                heap.push(((-1 * (dist[e.1] + next_e.1)), next_e.0));
            }
        }
    }
    dist
}

///最短経路計算(ワーシャルフロイド法)
pub fn warshall_floyd(graph: &mut Vec<Vec<isize>>) {
    for k in 0..graph.len() {
        for i in 0..graph.len() {
            for j in 0..graph.len() {
                graph[i][j] = cmp::min(graph[i][j], graph[i][k] + graph[k][j]);
            }
        }
    }
}

}
use graph::*;
use input::*;

fn main() {
    let (n, x, y): (usize, usize, usize);
    input!(n, x, y);

    let mut v = vec![vec![]; n];
    for i in 0..n - 1 {
        v[i].push((i + 1, 1));
        v[i + 1].push((i, 1));
    }

    v[x - 1].push((y - 1, 1));
    v[y - 1].push((x - 1, 1));

    let mut ans = vec![0; n + 1];
    for i in 0..n {
        let buf = dijkstra(&v, i);
        for i in buf {
            ans[i as usize] += 1;
        }
    }
    for i in 1..n {
        println!("{}", ans[i] / 2);
    }
}