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.*;
import java.util.TreeMap;
import java.util.Map;
 
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();
        TreeMap<Integer, Integer> map = new TreeMap<Integer, Integer>();
        
        for(int i=1; i<=N-1; i++){
            map.put(i, 0);
        }
        for(int i=1; i<=N-1; i++){
            for(int j=i+1; j<=N; j++){
                int r = Math.min(j - i, Math.abs(X - i) + Math.abs(j - Y) + 1);
                r = Math.min(r, Math.abs(Y - i) + Math.abs(j - X) + 1);
                if(map.containsKey(r)){
                    map.put(r, map.get(r) + 1);
                }
                else{
                    map.put(r, 1);
                }
            }
        }
        for(int x : map.keySet()){
            System.out.println(map.get(x));
        }
    }
}