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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace D
{
    class Program
    {
        static void Main(string[] args)
        {
            var nxy = Console.ReadLine().Split(' ');
            var n = int.Parse(nxy[0]);
            var x = int.Parse(nxy[1]);
            var y = int.Parse(nxy[2]);
            var count = new int[n - 1];
            for(int i = 1; i < n; i++)
            {
                for(int j = i + 1; j < n + 1; j++)
                {
                    count[Min3(Math.Abs(i - j), Math.Abs(i - x) + 1 + Math.Abs(y - j), Math.Abs(i - y) + 1 + Math.Abs(j - x)) - 1]++;
                }
            }
            foreach(int num in count)
            {
                Console.WriteLine(num);
            }

            Console.ReadKey();
        }

        static public int Min3(int a,int b,int c)
        {
            int min = int.MaxValue;
            min = Math.Min(a, b);
            min = Math.Min(min, c);
            return min;
        }
    }
}