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 q4
{
    class Program
    {
        static void Main(string[] args)
        {
            var input1 = Console.ReadLine().Split(' ').Select(x => Convert.ToInt32(x)).ToArray();
            var N = input1[0];
            var X = input1[1] - 1;
            var Y = input1[2] - 1;
            var warp = Y - X;
            var wt = (X + Y) / 2;

            Func<int, int, int> f = (I, J) =>
            {
                var d1 = Math.Abs(X - I);
                var d2 = Math.Abs(J - Y);
                return Math.Min(J - I, d1 + d2 + 1);
            };



            for (var k = 0; k < N - 1; k++)
            {
                var c = 0;
                for (var i = 0; i < N - 1; i++)
                {
                    for (var j = i + 1; j < N; j++)
                    {
                        var v = f(i, j);
                        if (v == k + 1)
                        {
                            c += 1;
                        }
                    }
                }
                Console.WriteLine(c);
            }
        }
    }
}