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

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

	    execute(sc.nextInt(),sc.nextInt(),sc.nextInt());
    }

    public static void execute(int size,int from,int to){
        int adjacencyMatrix[][] = new int[size][size];
        for(int i = 0;i < size ; i++ ){
            for(int j = 0;j < size ; j++ ){
                int adjacency = size;
                if(j - i == 1 || i - j == 1){
                    adjacency = 1;
                }
                if(i == from - 1 && j == to - 1){
                    adjacency = 1;
                }
                if(j == from - 1 && i == to - 1){
                    adjacency = 1;
                }
                if(i == j){
                    adjacency = 0;
                }
                adjacencyMatrix[i][j] = adjacency;
            }
        }

        for(int k = 0; k < size ; k++){
            for(int i = 0;i < size ; i++ ){
                for(int j = 0;j < size ; j++ ){
                    if(i <= j){
                        break;
                    }
                    adjacencyMatrix[i][j] = Math.min(
                            adjacencyMatrix[i][j],
                            adjacencyMatrix[i][k]+adjacencyMatrix[k][j]);
                }
            }
        }

        Map<Integer,Integer> countMap = new TreeMap<>();
        for(int i = 1; i <= size - 1 ; i++){
            countMap.put(i,0);
        }

        for(int i = 0;i < size ; i++ ){
            for(int j = 0;j < size ; j++ ){
                if(i <= j){
                    break;
                }
                Integer distanceResult = adjacencyMatrix[i][j];
                if(distanceResult != 0){
                    int count = countMap.get(distanceResult);
                    count++;
                    countMap.put(distanceResult,count);

                }
            }
        }
        for(Map.Entry<Integer,Integer> countEntry : countMap.entrySet()){
            System.out.println(countEntry.getValue());
        }

    }

}