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;

namespace ConsoleTest
{
    class Program
    {
        
        static void Main(string[] args)
        {
            //ShortestDistance(5, 2, 4, 1, 4);
            //return;
            int[] v = MyIo.Ints();
            int n = v[0];
            int x = v[1];
            int y = v[2];


            for(int k = 1; k <= n-1; k++)
            {
                Console.WriteLine(SumShortest(n,x,y,k));
            }
        }

        private static long SumShortest(int n, int x, int y, int k)
        {
            long result = 0;
            for (int i = 1; i <= n - 1; ++i)
            {
                for (int j = i + 1; j <= n; ++j)
                {
                    int s = ShortestDistance(n, x, y, i, j);
                    //Console.WriteLine(string.Format("shortestDistance [{0},{1}] {2}", i, j, s));
                    if (s == k) result++;
                }
            }
            return result;
        }

        private static int ShortestDistance(int n, int x, int y, int i, int j)
        {
            var basic = j - i;
            int toX = Math.Abs(x - i);
            int toY = Math.Abs(y - j);
            var branch = toX + toY+1;
            //Console.WriteLine(string.Format("SD for({4}, {5}) : {0}, {1}, {2}, {3}", basic, toX, toY, branch, i,j));
            return Math.Min(basic, branch);
        }
    }
    static class MyIo
    {
        public static int Int()
        {
            return int.Parse(Console.ReadLine());
        }
        public static int[] Ints()
        {
            return Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
        }
        public static int[][] MultiInts(int num)
        {
            var result = new int[num][];
            for(int i = 0; i < num; ++i)
            {
                result[i] = Ints();
            }
            return result;
        }
        public static T[] MultiItems<T>(int num, Func<string,T> parser)
        {
            var result = new T[num];
            for(int i =0; i < num; ++i)
            {
                result[i] = parser(Console.ReadLine());
            }
            return result;
        }
    }
}