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.Linq;
using System.Collections.Generic;

namespace ABC160
{
    class D
    {
        static void Main(string[] args)
        {
            var nxy = Console.ReadLine().Split().Select(long.Parse).ToArray();
            var n = nxy[0]; var x = nxy[1] - 1; var y = nxy[2] - 1;
            var dist1 = new long[n, n];
            for (int i = 0; i < n; i++)
            {
                for (int j = i; j < n; j++)
                {
                    if (i != j)
                    {
                        dist1[i, j] = Math.Min(Math.Abs(j - i), Math.Abs(x - i) + 1 + Math.Abs(j - y));
                        //dist1[i, j] = Math.Min(dist1[i, j], Math.Abs(y - i) + 1 + Math.Abs(j - x));
                    }
                }
            }

            /*
            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < n; j++)
                {
                    Console.Write(dist1[i, j]);
                }
                Console.WriteLine();
            }
            */

            var res = new long[n];
            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < n; j++)
                {
                    res[dist1[i, j]]++;
                }
            }

            for (int i = 1; i < n; i++)
            {
                Console.WriteLine(res[i]);
            }
        }
    }
}