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::io::Read;
use std::collections::BinaryHeap;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).ok();
    let mut it = buf.split_whitespace();
    let n = it.next().unwrap().parse::<usize>().unwrap();
    let x = it.next().unwrap().parse::<usize>().unwrap() - 1;
    let y = it.next().unwrap().parse::<usize>().unwrap() - 1;
    let mut res = vec![0; n];
    for s in 0..n {
        let mut d : Vec<i32> = vec![10000; n];
        d[s] = 0;
        let mut qu = BinaryHeap::new();
        qu.push((0i32, s));
        while !qu.is_empty() {
            let (_, pos) = qu.pop().unwrap();
            let mut update = |p : usize| {
                if d[p] > d[pos] + 1 {
                    d[p] = d[pos] + 1;
                    qu.push((-d[p], p));
                }
            };
            if pos > 0 { update(pos - 1) }
            if pos + 1 < n { update(pos + 1) }
            if pos == x { update(y) }
            if pos == y { update(x) }
        }
        for i in s+1..n { res[d[i] as usize] += 1 }
    }
    for i in 1..n { println!("{}", res[i]) }
}