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: Time Limit Exceeded)

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)
        {
            string line = Console.ReadLine();
            string[] strs = line.Split(' ');
            int N = int.Parse(strs[0]);
            int X = int.Parse(strs[1]) - 1;
            int Y = int.Parse(strs[2]) - 1;

            int[] distance = new int[N];
            for (int i = 0; i < N; i++) distance[i] = 0;

            int[] map = new int[N];
            for(int i = 0; i < N; i++)
            {
                //各頂点から各頂点への最短距離を出す
                for (int j = 0; j < N; j++) map[j] = N + 1;
                // 自分は0
                map[i] = 0;
                bool end = false;
                while(!end)
                {
                    end = true;
                    //まず隣から
                    for(int k = 0; k < N; k++)
                    {
                        if (k > 0 && map[k - 1] + 1 < map[k])
                        {
                            map[k] = map[k - 1] + 1;
                            end = false;
                        }
                        if (k < N - 1 && map[k + 1] + 1 < map[k])
                        {
                            map[k] = map[k + 1] + 1;
                            end = false;
                        }
                        if (k == X && map[Y] + 1 < map[k])
                        {
                            map[k] = map[Y] + 1;
                            end = false;
                        }
                        if (k == Y && map[X] + 1 < map[k])
                        {
                            map[k] = map[X] + 1;
                            end = false;
                        }
                    }
                }
                for(int j = 0; j < map.Length; j++)
                {
                    distance[map[j]]++;
                }
            }

            for(int i = 1; i < distance.Length; i++)
            {
                Console.WriteLine(distance[i] / 2);
            }

        }
    }
}