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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System.Linq;
using System.Collections.Generic;
using System;

public class Hello
{
    public static int[] dist;
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        dist = new int[n];
        var x = int.Parse(line[1]) - 1;
        var y = int.Parse(line[2]) - 1;
        var p = new List<int>[n];
        for (int i = 0; i < n; i++) p[i] = new List<int>();
        for (int i = 0; i < n - 1; i++)
        {
            p[i].Add(i + 1);
            p[i + 1].Add(i);
        }
        p[n - 1].Add(n - 2);
        p[x].Add(y);
        p[y].Add(x);
        for (int i = 0; i < n; i++) goBfs(p, n, i);
        var ans = new int[n -1];
        for (int i = 1; i < n; i++)
            ans[i - 1] = dist[i] / 2;
        Console.WriteLine(string.Join("\n",ans));
    }
    static void goBfs(List<int>[] p, int n, int s)
    {
        var q = new Queue<int>();
        q.Enqueue(s);
        var visited = new bool[n];
        visited[s] = true;
        var d = new int[n];
        d[s] = 0;
        while (q.Count() > 0)
        {
            var w = q.Dequeue();
            foreach (var x in p[w])
            {
                if (!visited[x])
                {
                    q.Enqueue(x);
                    visited[x] = true;
                    d[x] = d[w] + 1;
                    dist[d[x] ]++;
                }
            }
        }
    }
}