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

namespace AtCoderCs
{
    class Program
    {


        static List<int> Result = new List<int>();


        static void Main()
        {

            var Arg = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var Num = Arg[0];
            var X = Arg[1];
            var Y = Arg[2];

            for (int i = 1; i < Num; i++)
            {

                for (int j = i + 1; j <= Num; j++)
                {

                    if (i <= X)
                    {

                        if (j < X)
                        {

                            ResultEdit(j - i);

                        }
                        else if (j < Y)
                        {

                            int Compare1 = j - i;
                            int Compare2 = (X - i) + (Y - j) + 1;
                            ResultEdit(Compare1 > Compare2 ? Compare2 : Compare1);

                        }
                        else
                        {

                            ResultEdit((X - i) + (j - Y) + 1);

                        }

                    }
                    else if (i <= Y)
                    {

                        int Compare1, Compare2;
                        Compare1 = j - i;

                        if (j < Y)
                        {

                            Compare2 = (i - X) + (Y - j) + 1;

                        }
                        else
                            Compare2 = (i - X) + (j - Y) + 1;

                        ResultEdit(Compare1 > Compare2 ? Compare2 : Compare1);

                    }
                    else
                    {

                        ResultEdit(j - i);

                    }

                }

            }

            for (int i = 0; i < Num - 1; i++)
            {

                if (i < Result.Count) Console.WriteLine(Result[i]);
                else Console.WriteLine(0);

            }


        }

        static void ResultEdit(int Distance)
        {

            if (Result.Count < Distance) Result.Add(1);
            else Result[Distance - 1]++;

        }


}
}