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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author silviase
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DLine solver = new DLine();
        solver.solve(1, in, out);
        out.close();
    }

    static class DLine {
        public void solve(int testNumber, Scanner in, PrintWriter out) {

            int n = in.nextInt();
            int x = in.nextInt() - 1;
            int y = in.nextInt() - 1;
            int[] dist = new int[n + 1];
            Arrays.fill(dist, 0);
            for (int i = 0; i < n; i++) {
                for (int j = i + 1; j < n; j++) {
                    if (j <= x || y <= i) {
                        dist[j - i]++;
                    } else if (i <= x && y <= j) {
                        dist[(x - i) + 1 + (j - y)]++;
                    } else if (x < i && j < y) {
                        dist[j - i]++;
                    } else if (i <= x && j <= y) {
                        dist[Math.min(j - i, (x - i) + 1 + (y - j))]++;
                    } else if (x <= i && y <= j) {
                        dist[Math.min(j - i, i - x + 1 + (j - y))]++;
                    }
                }
            }

            for (int i = 0; i < n; i++) {
                if (i > 0) {
                    out.println(dist[i]);
                }
            }

        }

    }
}