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 ConsoleApp15
{
    class Class205
    {
        static bool[] used;
        static bool[] used2;
        static int[] count;
        static List<int>[] G;
        static void Main()
        {
            var NXY = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int N = NXY[0], X = NXY[1], Y = NXY[2];
            G = new List<int>[N];
            for (int i = 0; i < N; i++) G[i] = new List<int>();
            G[X - 1].Add(Y - 1);
            G[Y - 1].Add(X - 1);
            for(int i = 0; i < N-1; i++)
            {
                G[i].Add(i + 1);
                G[i + 1].Add(i);
            }

            count = new int[N];
            used2 = new bool[N];
            for(int i = 0; i < N; i++)
            {
                used = new bool[N];
                used2[i] = true;

                BFS(i);
            }
            for(int i = 0; i < N-1; i++)
            {
                
                Console.WriteLine(count[i]);
            }
        }
        static void BFS(int n)
        {
            used[n] = true;
            var que = new Queue<Tuple<int, int>>();
            que.Enqueue(Tuple.Create(n, 0));
            while (que.Count > 0)
            {
                var p = que.Dequeue();
                for(int i = 0; i < G[p.Item1 ].Count; i++)
                {
                    var e = G[p.Item1][i];
                    if (!used[e])
                    {
                        used[e] = true;
                        if (!used2[e]) count[p.Item2]++;
                        que.Enqueue(Tuple.Create(e, p.Item2 + 1));
                    }
                }
            }
        }
        static void DFS(int n,int c)
        {
            used[n] = true;
            if(!used2[n])
                count[c] += 1;
            for(int i = 0; i < G[n].Count; i++)
            {
                var e = G[n][i];
                if (used[e]) continue;
                DFS(e, c + 1);
            }
        }
    }
}