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: Wrong Answer)

import java.util.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class Main {
	public static void main(String[]args) {
		try(Scanner scan = new Scanner(System.in)){
			
			int N = scan.nextInt();
			int X = scan.nextInt();
			int Y = scan.nextInt();
			
			Map<Integer,Integer>map = new TreeMap<Integer,Integer>();
			int[] m = new int[2000];
			
			
			for(int i =1;i<=N-1;i++) {
				for(int j =i+1;j<=N;j++) {
					if(i<=X&&Y<=j) {
						int dist = (X-i)+1+(j-Y);
						m[dist]++;
						System.out.println(dist+" "+i+" "+j+" ");
						
					}else if(i>X&&Y<=j){
						int dist  =j-i;
						int xydist = i-X+1+j-Y;
						int d = dist<xydist?dist:xydist;
						m[d]++;
						System.out.println(dist+" "+i+" "+j+" ");	
					}else if(i<=X&&Y>j) {
						int dist  =j-i;
						int xydist = X-i+1+Y-j;
						int d = dist<xydist?dist:xydist;
						m[d]++;
						System.out.println(dist+" "+i+" "+j+" ");	
					}else if(i>X&&Y>j){
						int dist  =j-i;
						int xydist = i-X+1+Y-j;
						int d = dist<xydist?dist:xydist;
						m[d]++;
						System.out.println(dist+" "+i+" "+j+" ");	
					}
				}
				
			}
			
		
			
			for(int i = 1;i<N;i++) {
				System.out.println(m[i]);
			}
			
			
			
			
		}
		
		
	}
		

}