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 JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";
function main(input) {
  const inputs = input[0].trim().split(" ").map(i => parseInt(i));
  const n = inputs[0];
  const x = inputs[1];
  const y = inputs[2];

  let distances = [];
  for(let i=0;i<n-1;i++){
    distances[i] = 0;
  }

  for(let i=1;i<=n;i++){
    for(let j=i+1;j<=n;j++){
      let distance = Math.min(Math.abs(j-i), Math.abs(x-i)+Math.abs(y-j)+1);
      distances[distance-1]++;
    }
  }
  for(let i=0;i<n-1;i++){
    console.log(distances[i]);
  }
}
main(require('fs').readFileSync('/dev/stdin', 'utf8').trim().split("\n"));