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.Scanner;

public 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[] counter = new int[N];
	for(int i=1;i<N;i++){//頂点iから始まる
	    for(int k=1;k<=N-1;k++){//距離kのもの をカウント
		int nokori = k;
		int genzaichi = i;
		while(genzaichi < N){
		    if(genzaichi != X){
			genzaichi++;
			nokori--;
			if(nokori==0){
			    counter[k]++;
			    break;
			}
		    }else if(genzaichi == X){
			if(nokori >= Y-X){//遠回りしてYについてしまうのであればワープ
			    genzaichi = Y;
			    nokori--;
			    if(nokori==0){
				counter[k]++;
				break;
			    }
			}else{//ワープの有り無し選べる
			    int nokoriStock = nokori;
			    int genzaichiStock = genzaichi;
			    //ワープする
			    while(genzaichi < N){
				genzaichi = Y;
				nokori--;
				if(nokori==0){
				    counter[k]++;
				    break;
				}
			    }
			    
			    //ワープしない
			    while(genzaichiStock < N){
				genzaichiStock++;
				nokoriStock--;
				if(nokori==0){
				    counter[k]++;
				    break;
				}
			    }
			}
		    }
		}
	    }
	}
	for(int i=1;i<N;i++){
	    System.out.println(counter[i]);
	}
    }
}