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)

use proconio::input;
use std::collections::VecDeque;
use proconio::marker::Usize1;

fn push(dist: &mut Vec<usize>, queue: &mut VecDeque<usize>, v: usize, d: usize) {
  if dist[v] != usize::max_value() {
    return
  }
  dist[v] = d;
  queue.push_back(v);
}

fn main() {
  input! {
    K: usize,
    X: Usize1,
    Y: Usize1,
  }
  
  let mut answer: Vec<usize> = vec![0;K];
  for i in 0..K {
    let mut dist = vec![usize::max_value();K];
    let mut queue = VecDeque::new();
    push(&mut dist, &mut queue, i, 0);
    while queue.len() > 0 {
      let v = queue.pop_front().unwrap();
      let d = dist[v];
      if 0 != v { push(&mut dist, &mut queue, v-1, d+1); }
      if v+1 < K { push(&mut dist, &mut queue, v+1, d+1); }
      if v == X { push(&mut dist, &mut queue, Y, d+1); }
      if v == Y { push(&mut dist, &mut queue, X, d+1); }
    }
    
    for ii in dist {
      answer[ii] += 1;
    }
  }

  for i in 1..K {
    println!("{}", answer[i]/2);
  }
}