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.io.PrintWriter;
import java.util.*;

public class Main {

    Scanner sc = new Scanner(System.in);

    PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        new Main().run();
    }

    void run() {

        int n = sc.nextInt();
        int x = sc.nextInt()-1;
        int y = sc.nextInt()-1;

        int[][] dist = new int[n][n];

        for (int i=0; i<n-1; i++) {
            for (int j=i+1; j<n; j++) {
                int tmpD = j-i;
                if (j<=x || y<=i) {
                    dist[i][j] = tmpD;
                } else {
                    if (i<=x) {
                        tmpD = Math.min(tmpD, x-i+1+Math.abs(j-y));
                        dist[i][j] = tmpD;
                    } else {
                        tmpD = Math.min(tmpD, i-x+1+Math.abs(j-y));
                        dist[i][j] = tmpD;
                    }
                }
//                } else {
//                    tmpD = Math.min(tmpD, x-i+1+y-j>0 ? x-i+y-x+y-j:tmpD);
//                    tmpD = Math.min(tmpD, x-i+j-y+1>0 ? x-i+j-y+1:tmpD);
//                    tmpD = Math.min(tmpD, i-x+1+y-j>0 ? i-x+1+y-j:tmpD);
//                    tmpD = Math.min(tmpD, i-x+1+j-y>0 ? i-x+1+j-y:tmpD);
//                    dist[i][j] = tmpD;
//                }
            }
        }

//        for (int i=0; i<n-1; i++) {
//            for (int j=i+1; j<n-1; j++) {
//                out.print(dist[i][j]);
//
//            } out.println(dist[i][n-1]);
//        }
//        out.flush();

        int[] ans = new int[n-1];

        for (int i=0; i<n-1; i++) {
            for (int j=i+1; j<n; j++) {
                if (dist[i][j]!=0) {
                    int tmp = dist[i][j]-1;
                    ans[tmp]++;
                }
            }
        }

        StringBuilder sb = new StringBuilder();

        for (int i=0; i<n-1; i++) {
            sb.append(ans[i]+"\n");
        }



        out.print(sb.toString());
        out.flush();



    }

}