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::*;
use std::str::FromStr;
use std::collections::VecDeque;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

struct Main {
    n: usize,
    x: usize,
    y: usize,
    g: Vec<Vec<usize>>,
    d: Vec<Option<usize>>,
    res_d: Vec<Vec<Vec<usize>>>,
    contained: Vec<Vec<bool>>,
}
impl Main {
    fn bfs(&mut self, start: usize) {
        let mut q: VecDeque<usize> = VecDeque::new();
        q.push_back(start);
        let mut d: Vec<Option<usize>> = vec![None; self.n];
        d[start] = Some(0);
        while !q.is_empty() {
            let v = q.pop_front().unwrap();
            for &next_v in self.g[v].iter() {
                match d[next_v] {
                    None => {
                        q.push_back(next_v);
                        let new_d = d[v].unwrap() + 1;
                        d[next_v] = Some(new_d);
                        let new_res_d = if start < next_v {
                            vec![start, next_v]
                        } else {
                            vec![next_v, start]
                        };
                        if !self.contained[new_res_d[0]][new_res_d[1]] {
                            self.res_d[new_d].push(vec![start, next_v]);
                        }
                        self.contained[new_res_d[0]][new_res_d[1]] = true;
                        ()
                    }
                    Some(_) => (),
                }
            }
        }
//        println!("d: {:?}", d);
    }
    fn invoke(&mut self) {
        for i in 0..self.n {
            if i as i32 - 1 >= 0 {
                self.g[i].push(i - 1);
            }
            if i + 1 < self.n {
                self.g[i].push(i + 1);
            }
        }
        self.g[self.x-1].push(self.y-1);
        self.g[self.y-1].push(self.x-1);

        for i in 0..self.n {
            self.bfs(i);
        }

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

        for (i, res_d_one) in self.res_d.iter().enumerate() {
            if i == 0 {
                continue;
            }
            println!("{}", self.res_d[i].len());
        }
    }
}



fn main() {
    let n: usize = read();
    let x: usize = read();
    let y: usize = read();
    Main {
        n: n,
        x: x,
        y: y,
        g: vec![vec![]; n],
        d: vec![None; n],
        res_d: vec![vec![]; n],
        contained: vec![vec![false; n]; n],
    }.invoke()
}