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;
use std::collections::HashMap;

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() {
    type Graph = Vec<Vec<usize>>;
    let n: usize = read();
    let x: usize = read();
    let y: usize = read();
    let mut G: Graph = vec![Vec::new(); n];
    for i in 0..n-1 {
        G[i].push(i+1);
        G[i+1].push(i);
    }
    G[x-1].push(y-1);
    G[y-1].push(x-1);

    //各頂点からその他への頂点への最短距離を格納するvec 全要素は-1で初期化
    let mut dist:Vec<Vec<i32>> = vec![vec![-1; n];n];
    //探索状態管理queue
    let mut queue: VecDeque<usize> = VecDeque::new();

    //各頂点からその他への頂点への最短距離をBFSで求める
    for i in 0..n {
        dist[i][i] = 0;
        queue.push_back(i);

        while !queue.is_empty() {
            let v = queue.pop_front().unwrap();
            for nv in G[v].iter() {
                if dist[i][*nv] == -1 {
                    dist[i][*nv] = dist[i][v] + 1;
                    queue.push_back(*nv);
                }
            }
        }
    }

    //各距離ごとの組の数を管理するHashMap
    let mut scores = HashMap::new();

    //nC2の組み合わせを列挙
    for i in 0..n {
        for j in i+1..n{
            //println!("dist{}",dist[i][j] );
            //各距離ごとの個数をカウント
            let count = scores.entry(dist[i][j]).or_insert(0);
            *count += 1;
        }
    }
    //println!("{:?}",G);
    //println!("{:?}",dist);
    //頂点1からn-1までの個数を表示。データがない場合は0を表示。
    for i in 1..n {
        println!("{}", scores.get(&(i as i32)).unwrap_or(&0));
    }
}