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: Time Limit Exceeded)

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

public class Hello
{
    public static void Main()
    {
        hoge();
        //System.Console.ReadLine();
    }

    public static void hoge()
    {
        var vars = System.Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var n = vars[0];
        var x = vars[1];
        var y = vars[2];

        int[,] g = new int[n + 1,n + 1];
        int[] cost = new int[n];

        Stack<List<int>> stack = new Stack<List<int>>();
        
        for(int v = 1; v < n + 1; v++)
        {
            List<int> a = new List<int>();
            a.Add(v);
            stack.Push(a);
            while (stack.Count != 0)
            {
                var isadd = false;
                var node = stack.Pop();
                var current = node[node.Count - 1];
                var next = current + 1;
                if (!node.Contains(next) && next < n + 1)
                {
                    var cp = new List<int>(node);
                    cp.Add(next);
                    stack.Push(cp);
                    isadd = true;
                }
                next = current - 1;
                if (current != 1 && !node.Contains(next))
                {
                    var cp = new List<int>(node);
                    cp.Add(next);
                    stack.Push(cp);
                    isadd = true;
                }
                if (current == x)
                {
                    next = y;
                    if (!node.Contains(next))
                    {
                        var cp = new List<int>(node);
                        cp.Add(next);
                        stack.Push(cp);
                        isadd = true;
                    }
                }
                if (current == y)
                {
                    next = x;
                    if (!node.Contains(next))
                    {
                        var cp = new List<int>(node);
                        cp.Add(next);
                        stack.Push(cp);
                        isadd = true;
                    }
                }
                if (!isadd)
                {
                    for (int i = 0; i < node.Count - 1; i++)
                    {
                        for (int j = i + 1; j < node.Count; j++)
                        {
                            if (g[node[i], node[j]] == 0)
                            {
                                g[node[i], node[j]] = j - i;
                                g[node[j], node[i]] = j - i;
                                cost[j - i]++;
                            }
                            else if (g[node[i], node[j]] > j - i)
                            {
                                cost[g[node[i], node[j]]]--;
                                g[node[i], node[j]] = j - i;
                                g[node[j], node[i]] = j - i;
                                cost[j - i]++;
                            }
                        }
                    }
                }
            }
        }
        

        for(int i = 1; i < cost.Length; i++)
        {
            System.Console.WriteLine(cost[i]);
        }
    }
}