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: Runtime Error)

using System;
using System.Linq;
using System.Collections.Generic;


class Program
{
    static void Main(string[] args)
    {
        string[] NXY = Console.ReadLine().Split(' ');
        int N = int.Parse(NXY[0]);
        int X = int.Parse(NXY[1]);
        int Y = int.Parse(NXY[2]);

        int[] output = new int[N-1];
        int distance = 0;

        for(int i=0; i<=N-1; i++){
            for(int j=i+1; j<=N; j++){
                if(1 <= i && i <= X && 1 <= j && j <= X){
                    distance = j - i;
                }else if(1 <= i && i <= X && X < j && j < Y){
                    distance = Math.Min(j-i, X+Y-i-j+1);
                }else if(1 <= i && i <= X && Y <= j && j <= N){
                    distance = X-Y-i+j+1;
                }else if(X < i && i < Y && X < j && j < Y){
                    distance = Math.Min(j-i, -X+Y+i-j+1);
                }else if(X < i && i < Y && Y <= j && j <= N){
                    distance = Math.Min(j-i, -X-Y+i+j+1);
                }else{
                    distance = j - i;
                }

                output[distance-1] += 1;
            }
        }

        for(int i=0; i<N-1; i++){
            Console.WriteLine(output[i]);
        }
    }
}