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) {
        Scanner scanner = new Scanner(System.in);

        int n = scanner.nextInt();
        int x = scanner.nextInt();
        int y = scanner.nextInt();
        Map<Integer, Integer> map = new HashMap<>();
        for (int i = 1; i < n; i++) {
            map.put(i, 0);
        }

        for (int i = 1; i < n; i++) {
            for (int j = i + 1; j <= n; j++) {
                int length = calcLength(i, j, x, y);
                map.put(length, map.get(length) + 1);
            }
        }

        for (int i = 1; i < n; i++) {
            System.out.println(map.get(i));
        }
    }

    private static int calcLength(int i, int j, int x, int y) {
        int a = j - i;
        int b = Math.abs(x - i) + 1 + Math.abs(j - y);
//        int c = Math.abs(y - i) + 1 + Math.abs(j - x);

//        return Math.min(a, Math.min(b, c));
        return Math.min(a,b );
//        if (i <= x && j >= y) {
//            return ((j - i) - (y - x)) + 1;
//        } else if (i <= x && j < y) {
//            int lengthl = j - i;
//            int lengthr = (y - j) + (x - i) + 1;
//            return Math.min(lengthl, lengthr);
//        } else if (i > x && j >= y) {
//            int lengthl = j - i;
//            int lengthr = (i - x) + (j - y) + 1;
//            return Math.min(lengthl, lengthr);
//        } else {
//            return j - i;
//        }
    }
}