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

class Progaram
{
    static void Main(string[] args)
    {
        var l = Console.ReadLine().Split(' ').Select(k => int.Parse(k)).ToArray();
        var n = l[0]; var x = l[1]; var y = l[2];

        var nl = new List<int>();

        for (var now = 1; n > now; now++)
        {
            for (var seek = now + 1; n >= seek; seek++)
            {
                if (seek >= y && now <= x) nl.Add((seek - now) - (y - x) + 1);
                else if (seek >= y)
                {
                    if (y - now > now - x + 1) nl.Add((now - x + 1) + (seek - y));
                    else nl.Add(seek - now);
                }
                else if (now <= x)
                {
                    if (seek - x > y - seek + 1) nl.Add((y - seek + 1) + (x - now));
                    else nl.Add(seek - now);
                }
                else
                {
                    if ((now - x + 1) + (y - seek) < seek - now) nl.Add((now - x + 1) + (y - seek));
                    else nl.Add(seek - now);
                }
            }
        }

        for (var i = 1; n > i; i++)
        {
            Console.WriteLine(nl.Where(q => q == i).Count());
        }
    }
}