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: Time Limit Exceeded)

import java.util.*;
class Main{
  public static void main(String args[]){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt(),x = sc.nextInt(),y = sc.nextInt();
    int g[][]=new int[n][n];
    int count[]=new int[n];
    for(int i=0;i<n-1;i++){
      g[i][i+1]=1; g[i+1][i]=1;
    }
    g[x-1][y-1]=1; g[y-1][x-1]=1;

    for(int i=0;i<n;i++){
      int di[]=dijk(n,i,g);
      for(int j=i+1;j<n;j++){
        count[di[j]]++;
      }
    }
    for(int i=1;i<n;i++){
      pl(count[i]+"");
    }
  }

  public static int[] dijk(int n,int s,int g[][]){
    int dist[]=new int[n];
    boolean flg[]=new boolean[n];
    ArrayList<Integer> list = new ArrayList<Integer>();
    list.add(s);
    dist[s]=0;
    flg[s]=true;
    while(list.size()!=0){
      int num = list.get(0);
      list.remove(0);
      for(int i=0;i<n;i++){
        if(g[num][i]==1&&!flg[i]){
          list.add(i);
          flg[i]=true;
          dist[i]=dist[num]+1;
        }
      }
    }
    return dist;
  }

  public static void pr(String str){
    System.out.print(str);
  }
  public static void pl(String str){
    System.out.println(str);
  }
}