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)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
#![macro_use]

use std::cmp::*;
use std::collections::*;
use std::io::prelude::*;
use std::mem::*;
use std::num::*;
use std::slice::*;

const MOD: isize = 1_000_000_007;

fn main() {
    let (N, X, Y): (usize, usize, usize) = (read(), read::<usize>() - 1, read::<usize>() - 1);
    // g[k] : 最短距離がkの(i,j)の個数
    let mut g: Vec<usize> = vec![0usize; N + 1];
    // // X < Y である

    // let mut q: VecDeque<(usize, usize)> = VecDeque::new();
    // for i in 0..N - 1 {
    //     q.push_back((i + 1, 1));
    //     if (i == X) {
    //         q.push_back((Y, 1));
    //     }
    //     while let Some(x) = q.pop_front() {
    //         g[x.1] += 1;
    //         if x.0 < N - 1 {
    //             q.push_back((x.0 + 1, x.1 + 1));
    //         }
    //         if x.0 == X {
    //             q.push_back((Y, x.1 + 1));
    //         }
    //     }
    // }
    // for i in 1..N {
    //     println!("{}", g[i]);
    // }
    // ぜんてんもとめる
    let mut d = vec![vec![std::isize::MAX >> 2; N]; N];
    d[X][Y] = 1;
    let X = X as isize;
    let Y = Y as isize;
    for i in 0..N {
        for j in 0..N {
            d[i][j] = {
                let i = i as isize;
                let j = j as isize;
                min((j - i).abs(), (X - i).abs() + 1 + (Y - j).abs())
            }
        }
    }
    for i in 0..N {
        for j in i..N {
            g[d[i][j] as usize] += 1;
        }
    }
    for i in 1..N {
        println!("{}", g[i]);
    }
}
fn read<T>() -> T
where
    T: std::str::FromStr,
{
    let stdin = std::io::stdin();
    let next: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    next.parse().ok().unwrap()
}