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.Collections;

namespace Atcoder_0403
{
    class Program
    {
        static void Main(string[] args)
        {
            

            var input = Console.ReadLine().Split(' ');
            int _edgeCount = int.Parse(input[0]);
            int connectX = int.Parse(input[1]);
            int connectY = int.Parse(input[2]);

            int[] _resultCounts = new int[_edgeCount+1];//ここに結果を入れていく
            for (int j = 2; j <= _edgeCount; j++)//1<=i<j<=_edgeCountでループ　※ループの関係上jを先に回している
            {
                for(int i = 1; i < j; i++)
                {
                    int normalRoot = j - i;
                    int newRoot = Math.Abs(j - connectY) + Math.Abs(connectX - i) + 1;//xとiの距離+yとjの距離+1(xとyの短いほうの距離)
                    int length = (normalRoot > newRoot) ? newRoot : normalRoot;//小さいほうのrootを代入
                    _resultCounts[length]++;
                }
            }

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