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: Wrong Answer)

use std::io;
use std::str::FromStr;
use std::cmp::min;

fn input_tuple() -> (u64, u64, u64) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<u64> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1], vec[2])
}

fn calc_min(i: u64, j: u64, x: u64, y: u64) -> u64 {
    if i <= x {
        if j < x {
            return j - i;
        } else if j > y {
            return x - i + 1 + j - y;
        } else {
            return min(j - i, x - i + 1 + y - j);
        }
    } else if i > y {
        return j - i;
    } else {
        if j >= y {
            return min(j - i, i - x + 1 + j - y);            
        } else {
            return j - i;
        }
    }
}

fn main() {
    let (n, x, y) = input_tuple();
    let mut ans = vec![0; n as usize];
    for i in 1..n {
        for j in (i+1)..(n+1) {
            // println!("{}, {}, {}", i, j, calc_min(i, j, x, y));            
            ans[calc_min(i, j, x, y) as usize] += 1;
        }
    }
    for i in 1..n {
        println!("{}", ans[i as usize]);
    }
}