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 {

    static class Edge {
        int from, to;
        public Edge(int from, int to) {
            this.from = from;
            this.to = to;
        }
    }

    static void bfs(int start) {
        visited = new boolean[n];
        visited[start] = true;

        Deque<Integer> deque = new ArrayDeque<>();
        deque.offer(start);

        while (!deque.isEmpty()) {
            Integer node = deque.poll();
            List<Edge> edges = graph.get(node);

            for (Edge edge : edges) {
                if (visited[edge.to]) continue;
                dist[start][edge.to] = dist[start][node] + 1;
                visited[edge.to] = true;
                deque.offer(edge.to);
            }
        }
    }

    static void createGraph() {
        graph = new ArrayList<>();
        for (int i = 0; i < n; ++i) graph.add(new ArrayList<>());
        for (int i = 0; i < n - 1; ++i) {
            graph.get(i).add(new Edge(i, i + 1));
            graph.get(i + 1).add(new Edge(i + 1, i));
        }
    }

    static int n;
    static int x;
    static int y;
    static int[][] dist;
    static boolean[] visited;
    static List<List<Edge>> graph;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        x = sc.nextInt() - 1;
        y = sc.nextInt() - 1;
        createGraph();
        graph.get(x).add(new Edge(x, y));
        graph.get(y).add(new Edge(y, x));
        dist = new int[n][n];
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                dist[i][j] = 0;
            }
        }

        for (int i = 0; i < n; ++i) {
            bfs(i);
        }

        int[] arr = new int[n + 1];
        for (int i = 0; i < n; ++i) {
            for (int j = i + 1; j < n; ++j) {
                arr[dist[i][j]]++;
            }
        }

        for (int i = 1; i < n; ++i) {
            System.out.println(arr[i]);
        }
    }
}