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: Wrong Answer)

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 d = Y - X - 1;
            var g = new long[N, N];
            for (int i = 0; i < N; i++)
            {
                for (int j = i + 1; j < N; j++)
                {
                    // 通常の距離
                    //if ((j <= X - 1 && i <= X - 1)
                    //    || (j >= Y - 1 && i >= Y - 1))
                    //{
                    //    continue;
                    //}
                        g[i, j] = Math.Abs(j - i);

                    // 単純なショートカット
                    if (i <= X - 1 && j >= Y - 1)
                    {
                        g[i, j] = Math.Abs(j - i) - d;
                        continue;
                    }
                }
            }

            //for (var i = 0; i < N; i++)
            //{
            //    for (var j = i + 1; j < N; j++)
            //    {
            //        if (i < X - 3)
            //        {

            //        }
            //    }
            //}

            var ans = new StringBuilder();
            for (int i = 1; i < N; i++)
            {
                if (ans.Length > 0)
                {
                    ans.Append(Environment.NewLine);
                }
                ans.Append(GetCount(g, i));
            }

            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;
        }
    }
}