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::Read;
use std::collections::VecDeque;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

const INF: isize = 100_001;

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: isize = iterator.next().unwrap().parse().unwrap();
    let x: isize = iterator.next().unwrap().parse().unwrap();
    let y: isize = iterator.next().unwrap().parse().unwrap();

    let x = x - 1;
    let y = y - 1;

    let mut counts: Vec<usize> = vec![0; (n + 1) as usize];

    for sv in 0..n {
        let mut dist: Vec<isize> = vec![INF; n as usize];
        let mut q: VecDeque<isize> = VecDeque::new();

        dist[sv as usize] = 0;
        q.push_back(sv);

        while !q.is_empty() {
            let v = q.pop_front().unwrap();
            let d = dist[v as usize];
            if v - 1 >= 0 {
                if dist[(v - 1) as usize] == INF {
                    dist[(v - 1) as usize] = d + 1;
                    q.push_back(v - 1);
                }
            }
            if v + 1 < n {
                if dist[(v + 1) as usize] == INF {
                    dist[(v + 1) as usize] = d + 1;
                    q.push_back(v + 1);
                }
            }
            if v == x {
                if dist[y as usize] == INF {
                    dist[y as usize] = d + 1;
                    q.push_back(y);
                }
            }
            if v == y {
                if dist[x as usize] == INF {
                    dist[x as usize] = d + 1;
                    q.push_back(x);
                }
            }
        }

        for i in 0..n {
            counts[dist[i as usize] as usize] += 1;
        }
    }

    let mut ans = String::new();
    for i in 1..n {
        ans.push_str(&format!("{}\n", counts[i as usize] / 2))
    }
    return ans.trim().to_string();
}