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: Time Limit Exceeded)

use std::io::{self, BufRead};
use std::collections::HashSet;
use std::mem::swap;

fn main() {
  let stdin = io::stdin();
  let mut lines = stdin.lock().lines();
  let xs: Vec<i32> = lines.next().unwrap().unwrap().split(' ').map(|x| x.parse().unwrap()).collect();
  let n = xs[0];
  let x = xs[1] - 1;
  let y = xs[2] - 1;
  let mut min_dists = vec![vec![-1; n as usize]; n as usize];

  for beg in 0..n {
    let mut vacant: HashSet<i32> = (0..n).collect();
    vacant.remove(&beg);
    let mut ps = vec![beg; 1];
    let mut dist = 0;
    while !vacant.is_empty() {
      let mut qs = Vec::new();
      for p in &ps {
        if *p == x && vacant.contains(&y) {
          vacant.remove(&y);
          qs.push(y);
          if min_dists[beg as usize][y as usize] == -1 || dist < min_dists[beg as usize][y as usize] {
            min_dists[beg as usize][y as usize] = dist;
          }
        }
        let p1 = *p + 1;
        if p1 < n && vacant.contains(&p1) {
          vacant.remove(&p1);
          qs.push(p1);
          if min_dists[beg as usize][p1 as usize] == -1 || dist < min_dists[beg as usize][p1 as usize] {
            min_dists[beg as usize][p1 as usize] = dist;
          }
        }
        let p2 = *p - 1;
        if p2 >= 0 && vacant.contains(&p2) {
          vacant.remove(&p2);
          qs.push(p2);
          if min_dists[beg as usize][p2 as usize] == -1 || dist < min_dists[beg as usize][p2 as usize] {
            min_dists[beg as usize][p2 as usize] = dist;
          }
        }
      }
      swap(&mut ps, &mut qs);
      dist += 1;
    }
  }

  for k in 0..(n-1) {
    let mut count = 0;
    for i in 0..n {
      for j in (i+1)..n {
        if min_dists[i as usize][j as usize] == k {
          count += 1;
        }
      }
    }
    println!("{}", count);
  }
}