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.Diagnostics;
using System.Linq;
using System.Text;

namespace AtCoder.D
{
    internal static class CR
    {
        public static string GetText() { return Console.ReadLine(); }
        public static List<string> GetTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long GetLong() { return long.Parse(Console.ReadLine()); }
        public static List<long> GetLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }
    }

    public class Program
    {
        public static long N { get; private set; }
        public static long X { get; private set; }
        public static long Y { get; private set; }

        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var inputs = CR.GetLongs();
            N = inputs[0];
            X = inputs[1];
            Y = inputs[2];

            var xIndex = X - 1;
            var yIndex = Y - 1;

            var d = Y - X - 1;
            var g = new long[N, N];
            var answer = new long[N - 1];
            for (int i = 0; i < N; i++)
            {
                for (int j = i + 1; j < N; j++)
                {
                    if (j <= xIndex)
                    {
                        if (i <= xIndex)
                        {
                            // 通常の距離
                            g[i, j] = Math.Abs(j - i);
                            answer[g[i, j]]++;
                            continue;
                        }
                        // 考慮不要
                        //if (xIndex < i && i < yIndex)
                        //{
                        //    continue;
                        //}
                        //if (yIndex <= j)
                        //{
                        //    continue;
                        //}
                    }
                    else if (xIndex < j && j < yIndex)
                    {
                        if (i <= xIndex)
                        {
                            var straight = Math.Abs(j - i);
                            var maybe = xIndex - i + yIndex - j + 1;
                            g[i, j] = Math.Min(straight, maybe);
                            answer[g[i, j]]++;
                            continue;
                        }
                        if (xIndex < i && i < yIndex)
                        {
                            // TODO
                            var straight = Math.Abs(j - i);
                            var maybe = i - xIndex + yIndex - j + 1;
                            g[i, j] = Math.Min(straight, maybe);
                            answer[g[i, j]]++;
                            continue;
                        }
                        // 考慮不要
                        //if (yIndex <= j)
                        //{
                        //    continue;
                        //}
                    }
                    else
                    {
                        if (i <= xIndex)
                        {
                            // 単純なショートカット
                            g[i, j] = Math.Abs(j - i) - d;
                            answer[g[i, j]]++;
                            continue;
                        }
                        if (xIndex < i && i < yIndex)
                        {
                            var straight = Math.Abs(j - i);
                            var maybe = i - xIndex + j - yIndex + 1;
                            g[i, j] = Math.Min(straight, maybe);
                            answer[g[i, j]]++;
                            continue;
                        }
                        if (yIndex <= i)
                        {
                            // 通常の距離
                            g[i, j] = Math.Abs(j - i);
                            answer[g[i, j]]++;
                            continue;
                        }
                    }

                }
            }

            var ans = new StringBuilder();
            for (int i = 1; i < N - 1; i++)
            {
                ans.AppendLine(answer[i].ToString());
            }
            ans.Append("0");

            return ans.ToString();
        }

        private static long GetCount(long[,] g, int value)
        {
            var count = 0L;
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < N; j++)
                {
                    if (g[i, j] == value)
                    {
                        count++;
                    }
                }
            }
            return count;
        }
    }
}