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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;

class Program
{
    static void Main(string[] args)
    {
        var NXY = ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
        var (N, X, Y) = (NXY[0], NXY[1] - 1, NXY[2] - 1);

        var list = new List<int>[N];

        for (int i = 0; i < N; i++)
        {
            list[i] = new List<int>();
            if (i < N - 1)
                list[i].Add(i + 1);
            if (0 < i)
                list[i].Add(i - 1);
        }
        list[X].Add(Y);
        list[Y].Add(X);

        var ans = new int[N];

        for (int i = 0; i < N; i++)
        {
            var dist = Enumerable.Repeat(-1, N).ToArray();
            dist[i] = 0;

            var q = new Queue<int>();
            q.Enqueue(i);

            while (q.Count > 0)
            {
                var v = q.Dequeue();

                foreach (var next in list[v])
                {
                    if (dist[next] < 0)
                    {
                        dist[next] = dist[v] + 1;
                        q.Enqueue(next);
                    }
                }
            }

            for (int j = 0; j < N; j++)
                ans[dist[j]]++;
        }

        for (int i = 0; i < N; i++)
            ans[i] /= 2;

        for (int i = 1; i < N; i++)
            WriteLine(ans[i]);
    }
}