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.Text;
using System.Collections.Generic;
using static System.Math;
using System.Linq;
using static System.Array;
using System.Runtime.Serialization.Formatters.Binary;
using System.IO;

namespace AtcoderExpress
{


    class Program2
    {
        static long mod = 1000000007;
        static void Main(string[] args)
        {
            var NXY = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var N = NXY[0];
            var X = NXY[1];
            var Y = NXY[2];
            var sa = Y - X-1;

            var map = new long[N + 1, N + 1];
            
            //init
            for (int i = 1; i <= N; i++)
            {
                for (int j = 1; j <= N; j++)
                {
                    map[i, j] = Abs(j - i);
                }
            }
            map[X, Y] = 1;
            for (int i = 1; i <= N; i++)
            {
                for (int j = 1; j <= N; j++)
                {
                    map[i, j] = Min(map[i, j], map[i, X] + map[Y, j] + 1);
                    map[i, j] = Min(map[i, j], map[i, Y] + map[X, j] + 1);
                }
            }

                    var ans = new long[N];
            for (int i = 1; i <= N; i++)
            {
                for (int j = i+1; j <= N; j++)
                {
                    //if(i <= X && j >= Y)
                    //{
                    //    map[i, j] -= sa;

                    //}
                    if (map[i, j] > 0)
                    {
                        ans[map[i, j]]++;
                    }
                    //Console.Write(map[i, j]);
                }
               // Console.WriteLine();
            }


            for (int i = 1; i < N; i++)
            {
                Console.WriteLine(ans[i]);
            }
            
        }
    }
}