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)

// https://atcoder.jp/contests/abc160/tasks/abc160_d

use proconio::fastout;
use proconio::input;

#[fastout]
fn main() {
    input! {
        n: usize,
        x: usize, y: usize,
    }
    let mut vec = vec![0; n];

    for i in 1..=n - 1 {
        for j in i + 1..=n {
            vec[dist(i, j, x, y)] += 1;
        }
    }
    for k in 1..=n - 1 {
        println!("{}", vec[k]);
    }
}

fn dist(i: usize, j: usize, x: usize, y: usize) -> usize {
    (j - i).min(abs_diff(x, i) + 1 + abs_diff(y, j))
}

fn abs_diff(a: usize, b: usize) -> usize {
    if a > b {
        a - b
    } else {
        b - a
    }
}