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::cmp;
use std::io::stdin;

fn calc_num_i_j_for_k(x: i32, y: i32, k: i32, n: i32) -> i32 {
    let mut res = 0;
    for i in 1..n {
        for j in i + 1..n + 1 {
            let min_dist = cmp::min(j - i, (x - i).abs() + (j - y).abs() + 1);
            if min_dist == k {
                res += 1;
            }
        }
    }

    res
}

fn main() {
    let mut s = String::new();
    stdin().read_line(&mut s).ok();
    let in_vec: Vec<i32> = s
        .trim()
        .split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect();
    let n = in_vec[0];
    let x = in_vec[1];
    let y = in_vec[2];

    let mut reses: Vec<i32> = Vec::new();
    for k in 1..n {
        reses.push(calc_num_i_j_for_k(x, y, k, n));
    }

    for i_res in reses {
        println!("{}", i_res);
    }
}