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

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")
}

fn main() {
    let in_n: usize = read();
    let in_x: usize = read();
    let in_y: usize = read();
    let x = in_x - 1;
    let y = in_y - 1;
    let mut table = Vec::new();
    let mut updated = vec![false; in_n];

    for _ in 0..in_n {
        table.push(vec![in_n; in_n]);
    }

    for i in 0..in_n {
        table[i][i] = 0;
    }

    let mut queue = VecDeque::new();

    updated[0] = true;
    queue.push_back(0usize);

    while !queue.is_empty() {
        let i = queue.pop_front().unwrap();

        if !updated[i] {
            continue;
        }

        updated[i] = false;

        for j in 0..in_n {
            let d = table[j][i] + 1;

            if i > 0 && table[j][i - 1] > d {
                table[j][i - 1] = d;
                table[i - 1][j] = d;
                updated[i - 1] = true;
                queue.push_front(i - 1);
            }

            if i < in_n - 1 && table[j][i + 1] > d {
                table[j][i + 1] = d;
                table[i + 1][j] = d;
                updated[i + 1] = true;
                queue.push_front(i + 1);
            }

            if i == x && table[j][y] > d {
                table[j][y] = d;
                table[y][j] = d;
                updated[y] = true;
                queue.push_front(y);
            }

            if i == y && table[j][x] > d {
                table[j][x] = d;
                table[x][j] = d;
                updated[x] = true;
                queue.push_front(x);
            }
        }
    }

    let mut count = vec![0; in_n];

    for i in 0..in_n {
        for j in i + 1..in_n {
            count[table[i][j]] += 1;
        }
    }

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