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;

namespace D
{
	class Program
	{

		static void printMatrix(List<List<int>> matrix){
			for (int i = 0; i < matrix.Count; i++)
			{
				for (int j = 0; j < matrix[i].Count; j++)
				{
					Console.Write(matrix[i][j]);
					Console.Write(' ');
				}
				Console.Write('\n');
			}
			Console.Write('\n');
		}


		static void Main(string[] args)
		{
			string[] tmp_str = Console.ReadLine().Split(' ');
			int N = int.Parse(tmp_str[0]);
			int X = int.Parse(tmp_str[1]);
			int Y = int.Parse(tmp_str[2]);
			X--;
			Y--;

			// 距離配列
			List<List<int>> matrix = new List<List<int>>();
			// 初期化
			for (int i = 0; i < N; i++)
			{
				List<int> tmp_list = new List<int>();
				for (int j = 0; j < N; j++)
				{
					tmp_list.Add(Math.Abs(i-j));
				}
				matrix.Add(tmp_list);
			}
			matrix[X][Y] = 1;
			matrix[Y][X] = 1;

			// デバッグ表示
			// printMatrix(matrix);

			// やろうとしたけどTLEした
			// // ワーシャルフロイド法
			// for (int i = 0; i < N; i++)
			// {
			// 	for (int j = 0; j < N; j++)
			// 	{
			// 		for (int k = 0; k < N; k++)
			// 		{
			// 			matrix[i][j] = matrix[j][i] = Math.Min(matrix[i][j], matrix[i][k] + matrix[k][j]);
			// 		}
			// 	}
			// }

			// 解放
			for (int i = 0; i < N; i++)
			{
				for (int j = 0; j < N; j++)
				{
					matrix[i][j] = Math.Min(matrix[i][j], Math.Min(Math.Abs(X-i)+1+Math.Abs(Y-j), Math.Abs(Y-i)+1+Math.Abs(X-j)));
				}
			}

			// デバッグ表示
			// printMatrix(matrix);

			// 1~N-1までを数える
			List<int> ans = new List<int>();
			for (int i = 0; i < N; i++)
			{
				ans.Add(0);
			}
			for (int imatrix = 0; imatrix < N; imatrix++)
			{
				for (int jmatrix = 0; jmatrix < N; jmatrix++)
				{
					ans[matrix[imatrix][jmatrix]]++;
				}
			}
			for (int k = 1; k < N; k++)
			{
				Console.WriteLine(ans[k] / 2);
			}
		}
	}
}