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 AtcoderBeginnerContest160.Questions;
using AtcoderBeginnerContest160.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace AtcoderBeginnerContest160.Questions
{
    public class QuestionD : AtCoderQuestionBase
    {
        int[] minDistanceCount = null;
        int[] distances = null;
        readonly Queue<int> todo = new Queue<int>();
        int n;
        int x;
        int y;


        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nxy = inputStream.ReadIntArray();
            n = nxy[0];
            x = nxy[1];
            y = nxy[2];

            minDistanceCount = new int[n];
            distances = new int[n + 1];

            for (int i = 1; i <= n; i++)
            {
                Search(i);
            }

            for (int i = 1; i < n; i++)
            {
                yield return minDistanceCount[i] / 2;
            }
        }

        void Search(int startIndex)
        {
            todo.Clear();
            todo.Enqueue(startIndex);

            InitializeDistance();
            distances[startIndex] = 0;

            while (todo.Count > 0)
            {
                var current = todo.Dequeue();
                var nextDistance = distances[current] + 1;

                if (current > 1 && distances[current - 1] < 0)
                {
                    distances[current - 1] = nextDistance;
                    minDistanceCount[nextDistance] += 1;
                    todo.Enqueue(current - 1);
                }
                if (current < n && distances[current + 1] < 0)
                {
                    distances[current + 1] = nextDistance;
                    minDistanceCount[nextDistance] += 1;
                    todo.Enqueue(current + 1);
                }
                if (current == x && distances[y] < 0)
                {
                    distances[y] = nextDistance;
                    minDistanceCount[nextDistance] += 1;
                    todo.Enqueue(y);
                }
                if (current == y && distances[x] < 0)
                {
                    distances[x] = nextDistance;
                    minDistanceCount[nextDistance] += 1;
                    todo.Enqueue(x);
                }
            }
        }

        void InitializeDistance()
        {
            for (int i = 0; i < distances.Length; i++)
            {
                distances[i] = -1;
            }
        }
    }
}


namespace AtcoderBeginnerContest160
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionD();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace AtcoderBeginnerContest160.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace AtcoderBeginnerContest160.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion