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;
class Program
{
	static void Main(string[] args)
	{
		string[]str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		int X = int.Parse(str[1])-1;
		int Y = int.Parse(str[2])-1;
		long[]A = new long[N];
		for(var i=0;i<N;i++){
			for(var j=i+1;j<N;j++){
				if(i<=X && j<=X){
					A[Math.Abs(j-i)]++;
				} else if(i>=Y && j>=Y){
					A[Math.Abs(j-i)]++;
				} else if(i<=X && j>=Y){
					A[Math.Abs(X-i)+Math.Abs(Y-j)+1]++;
				} else {
                  	A[Math.Min(Math.Abs(i-j),Math.Abs(X-i)+1+Math.Abs(Y-j))]++;
                }
			}
		}
		for(var i=1;i<=N-1;i++){
			Console.WriteLine(A[i]);
		}
	}
}