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.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		int x = sc.nextInt();
		int y = sc.nextInt();
		
		int[] result = new int[n];
		result[1] = n;
		
		for (int i = 1; i < n; i++) {
			int first = x - i;
			int second = y - x;
			int third = n - y;

			for (int k = 2; i + k <= n; k++) {
				if (first < 0 && k <= n - i) {
					result[k]++;
					continue;
				}
				
				if (k <= first) {
					result[k]++;
					continue;
				}
				
				int nokori = k - first;
				//X → Y → 大きい値の場合
				if ((nokori > 1) && (nokori - 1 <= third)) {
					result[k]++;
				}
				
				double middle = (y + 1 - x) / 2.0;
				if (nokori < middle) {
					result[k] += 2;
				} else if (nokori == middle) {
					result[k]++;
				}
			}
		}
		
		for (int i = 1; i < n; i++) {
			System.out.println(result[i]);
		}
	}
}