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.*;
public class Main {
    public static void main(String[] args){
      // 入力
      Scanner sc = new Scanner(System.in);
      int N = sc.nextInt();
      int X = sc.nextInt();
      int Y = sc.nextInt();
      
      // 算出
      int[] dist = new int[N];
      for(int i = 0; i < N; i++){
        dist[i] = 0;
      }
      
      for(int i = 1; i <= N-1; i++){
        for(int j = i+1; j <= N; j++){
          int index = getDistance(i, j, X, Y);
          dist[index]++;
        }
      }
      
      // 出力
      for(int i = 1; i < N; i++){
        System.out.println(dist[i]);
      }
    }
    
    // 2頂点間の最短距離を求める関数
    public static int getDistance(int p1, int p2, int X, int Y){
      // 近道を使用しない場合の距離
      int dist1 = p2 - p1;
      
      // 近道を使用する場合の距離
      int dist2 = abs(X - p1) + abs(Y - p2) + 1;
      
      if(dist1 < dist2){
        return dist1;
      }else{
        return dist2;
      }
    }
    
    // 絶対値を求める関数
    public static int abs(int num){
      if(num < 0){
        return num * (-1);
      }else{
        return num;
      }
    }

}