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 Java7 (OpenJDK 1.7.0) (judge verdict: Runtime Error)

import java.io.*;
import java.lang.Math;
public class Main
{
  public static void main(String args[])throws Exception
  {
    int n,x,y,i,j;
    int one=0,two=0,three=0,min=0;
    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    n=Integer.parseInt(br.readLine());
    x=Integer.parseInt(br.readLine());
    y=Integer.parseInt(br.readLine());
    int arr[]=new int[n+1];
    for(i=1;i<=n;i++)
    {
      for(j=i+1;j<=n;j++)
      {
        one=j-i;
        two=Math.abs(x-i)+1+Math.abs(j-y);
		
        three=Math.abs(y-i)+1+Math.abs(j-x);
		
        if(one<=two && one<=three)
          min=one;
        else if(two<=one && two<=three)
          min=two;
        else
          min=three;
        arr[min]++;
	  }
	}
	for(i=1;i<n;i++)
	{
		
			System.out.println(arr[i]);
	}
  }
}