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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
#![allow(unused_variables)]

use itertools::Itertools;
use proconio::marker::*;
use proconio::*;
use std::collections::VecDeque;

#[fastout]
fn main() {
    input! {
        n: usize,
        x: Usize1,
        y: Usize1,
    }
    // annotate for rust-analyzer
    let n: usize = n;
    let x: usize = x;
    let y: usize = y;

    let mut dist = vec![vec![-1i32; n]; n];
    for i in 0..n {
        let mut q = VecDeque::new();
        dist[i][i] = 0;
        q.push_back(i);
        while q.len() > 0 {
            let cur = q.pop_front().unwrap();
            let mut nexts = Vec::new();
            if cur > 0 {
                nexts.push(cur - 1);
            }
            if cur < n - 1 {
                nexts.push(cur + 1);
            }
            if cur == x {
                nexts.push(y);
            }
            if cur == y {
                nexts.push(x);
            }
            for next in nexts {
                if dist[i][next] == -1 {
                    dist[i][next] = dist[i][cur] + 1;
                    q.push_back(next);
                }
            }
        }
    }

    let mut anss = vec![0; n];
    for i in 0..n - 1 {
        for j in i + 1..n {
            anss[dist[i][j] as usize] += 1;
        }
    }
    for i in 1..n {
        println!("{}", anss[i]);
    }
}