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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*; 

class Main{
public static void main(String[] args){
	Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int x=sc.nextInt();
		int y=sc.nextInt();
  		int[] a=new int[n-1];
  		int e=0;
  		int m=0;
  
  		for(int c=1;c<=n;c++){
        for(int d=c+1;d<=n;d++){
        	if(c<=x&&y<=d){
            	a[(d-y)+1+(x-c)-1]++;
            }else if(c<=x&&d<=x){
            	a[d-c-1]++;
            }else if(c<=x&&x<d){
            	 e=(x-c)+1+(y-d);
               m=Math.min(e,(d-c));
              a[m-1]++;
            }else if(c>=y&&d>=y){
            	a[d-c-1]++;
            }else if(c>x&&d<=y){
            	e=(c-x)+1+(y-d);
                m=Math.min(e,(d-c));
              	a[m-1]++;
            }else{
            	e=(c-x)+1+(d-y);
                m=Math.min(e,(d-c));
              	a[m-1]++;
            }
        }
        }

  
  		for(int ans:a){
        System.out.println(ans);
        }
    }
}