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[]) throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int x = sc.nextInt();
        int y = sc.nextInt();
        Map<Integer, List<Integer>> graph = new HashMap<>();
        for(int i = 1; i <= n; i++) {
        	graph.put(i, new ArrayList<>());
        }
        for(int i = 1; i < n; i++) {
        	graph.get(i).add(i + 1);
        	graph.get(i + 1).add(i);
        }
        graph.get(x).add(y);

        Map<Integer, Integer> cntMap = new HashMap<>();
        Queue<Integer> queue = new LinkedList<>();
        Set<Integer> visited = new HashSet<>();
        for(int i = 1; i < n; i++) {
	        queue.clear();
	        queue.offer(i);
	        visited.clear();
	        visited.add(i);
	        int dist = 0;
	        while(!queue.isEmpty()) {
	        	int size = queue.size();
	        	for(int j = 0; j < size; j++) {
	        		int node = queue.poll();
	        		if(node > i)
	        		    cntMap.put(dist, cntMap.getOrDefault(dist, 0) + 1);
	        		if(!graph.containsKey(node)) continue;
	        		for(int adj : graph.get(node)) {
	        			if(visited.contains(adj)) continue;
	        			queue.offer(adj);
	        			visited.add(adj);
	        		}
	        	}
	        	dist++;
	        }
        }
        for(int i = 1; i < n; i++)
        	System.out.println(cntMap.getOrDefault(i, 0));
    }
}