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.Linq;
using System.Text;

public class MainClass
{
	public const long Giri = 1000000007;
	public const long DpInf = 99999999999999;
	
	public class Node
	{
		public int Index{get;set;}
		public List<int> Edges {get;set;}
		public int Distance {get;set;}
		public bool Visited {get;set;}
	}
	
	public static void Main(string[] args)
	{
		var p = Input().ToInt();
		var n = p[0];
		var x = p[1] - 1;
		var y = p[2] - 1;
		
		var nodes = new Node[n];
		for(int i = 0; i < n; i++)
		{
			var e = new Node(){Index = i, Edges = new List<int>(), Distance = -1};
			if(i != n-1)
				e.Edges.Add((i+1)%n);
			if(i != 0)
				e.Edges.Add((i+(n-1))%n);
			nodes[i] = e;
		}
		nodes[x].Edges.Add(y);
		nodes[y].Edges.Add(x);
		
		var map = new long[n];
		for(int i = 0; i < n; i++)
		{
			BFS(nodes, i, 0);
			
			for(int j = i+1; j < n; j++)
			{
				var d = nodes[j].Distance;
				map[d]++;
			}
			for(int j = 0; j < n; j++)
				nodes[j].Distance = -1;
		}
		for(int i = 1; i < map.Length; i++)
			Console.WriteLine(map[i]);
	}
	
	static void BFS(Node[] nodes, int index, int far)
	{
		if(nodes[index].Distance != -1 && nodes[index].Distance <= far)
			return;
		nodes[index].Distance = far;
		foreach(var k in nodes[index].Edges)
		{
			BFS(nodes, k, far + 1);
		}
	}
	
	static long GCD(long a, long b)
	{
		var v = new[] { a, b };
		while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
		return v[0];
	}
	public static string[] Input() { return Console.ReadLine().Split(); }
}

public static class Smarter
{
	public static int ToInt(this string str) { return int.Parse(str); }
	public static long ToLong(this string str) { return long.Parse(str); }
	public static int[] ToInt(this string[] str, int offset = 0)
	{
		var r = new int[str.Length];
		for(int i = 0; i < str.Length; i++) r[i] = str[i].ToInt() + offset;
		return r;
	}
}