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;
class Program
{
	static void Main()
	{
        string[] input = Console.ReadLine().Split(' ');
        int n = int.Parse(input[0]);
        int x = int.Parse(input[1]);
        int y = int.Parse(input[2]);
        int[] result = new int[n * 2];
        int kouho1 = 0;
        int kouho2 = 0;
        int kouho3 = 0;
        int kyori = 0;
        for (int i = 1; i <= n - 1; i++) {
            // Console.WriteLine("test");
            for (int j = i+1; j <= n; j++) {
                kyori = 0;
                if (i == j || i >= j){
                    continue;
                } else {
                    //Console.WriteLine(i + "," + j);
                    kouho1 = j - i;
                    kouho2 = Math.Abs(x - i) + 1 + Math.Abs(j - y);
                    kouho3 = Math.Abs(y - i) + 1 + Math.Abs(j - x);
                    //Console.WriteLine(kouho1 + "," + kouho2 + "," + kouho3);
                    //Console.WriteLine("test5");
                    if (kouho1 > kouho2)
                    {
                        kyori = kouho2;
                        //Console.WriteLine(kyori);
                    } else {
                        kyori = kouho1;
                    }
                    /* else {
                        kyori = kouho3;
                    }
                    */
                    if (kyori > kouho3){
                        kyori = kouho3;
                        //Console.WriteLine(kyori);
                    }
                    //Console.WriteLine(kyori);
                    // Console.WriteLine("test6");
                    //Console.WriteLine(kyori);
                    // Console.WriteLine(n);
                    result[kyori] = result[kyori] + 1;
                    //Console.WriteLine("test3");
                }
            }
            //Console.WriteLine("test4");
        }
        for (int k = 1; k < n; k++) {
            Console.WriteLine(result[k]);
        }
        //Console.WriteLine(result);
	}

    static string equalCheck(string target1,string target2){
        if (target1 == target2){
            return "Yes";
        } else {
            return "No";
        }
    }
/*
    static int NotEqualCheck(int target1,int target2,int shokiti){
        if (target1 > target2){
            return target2;
        } else {
            return shokiti;
        }
    }
*/
}