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: Time Limit Exceeded)

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

pub 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")
}

pub fn read_n<T: FromStr>(n: usize) -> Vec<T> {
    read_n_logic::<T>(n, vec![])
}

pub fn read_n_logic<T: FromStr>(n: usize, mut a: Vec<T>) -> Vec<T> {
    match n {
        0 => a,
        _ => {
            a.push(read::<T>());
            read_n_logic(n - 1, a)
        }
    }
}
use std::cmp::{max, min};
use std::collections::HashMap;
use std::collections::VecDeque;

fn main() {
    let n: usize = read();
    let x: i64 = read();
    let y: i64 = read();
    let mut map: HashMap<i64, Vec<i64>> = HashMap::new();
    for i in 1..n {
        let a = i as i64;
        let b = i as i64 + 1;
        hashmap_process(&mut map, a, b);
    }
    hashmap_process(&mut map, x, y);

    let mut cnt: Vec<i64> = vec![0; n + 1];

    for i in 1..n + 1 {
        let result = bfs(i as i64, &map, n);
        for i in 0..result.len() {
            let ir = result[i];
            if ir < 1 {
                continue;
            }
            cnt[ir as usize] += 1;
        }
    }
    for i in 0..cnt.len() {
        if i == 0 || i == cnt.len() - 1 {
            continue;
        }

        println!("{}", cnt[i] / 2);
    }
}

fn bfs(node: i64, map: &HashMap<i64, Vec<i64>>, n: usize) -> Vec<i64> {
    // (node, depth)
    let mut vd: VecDeque<(i64, i64)> = VecDeque::new();
    let mut done: Vec<i64> = vec![];
    let mut ans: Vec<i64> = vec![-1; n + 1];
    vd.push_back((node, 0));
    while !vd.is_empty() {
        let current = vd.pop_front().unwrap();
        let vcurrent: &Vec<i64> = map.get(&current.0).unwrap();
        done.push(current.0);
        ans[current.0 as usize] = current.1;
        for i in vcurrent {
            if !done.contains(i) {
                ans[*i as usize] = current.1 + 1;
                vd.push_back((*i, current.1 + 1));
                done.push(*i);
            }
        }
    }
    ans
}

fn hashmap_process(map: &mut HashMap<i64, Vec<i64>>, a: i64, b: i64) {
    if map.contains_key(&a) {
        let current = map.get_mut(&a).unwrap();
        current.push(b);
    } else {
        map.insert(a, vec![b]);
    }

    if map.contains_key(&b) {
        let current = map.get_mut(&b).unwrap();
        current.push(a);
    } else {
        map.insert(b, vec![a]);
    }
}