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[] args)
	{
      	string[] input = Console.ReadLine().Split(' ');
		int n = int.Parse(input[0]);
		int x = int.Parse(input[1]);
		int y = int.Parse(input[2]);
        int[] cnt = new int[n-1];
        double midxy = (double)(x+y-1)/2;

        for(int g = 0; g < n-1; g++) cnt[g] = 0;
        for(int i = 0; i < n-1; i++)
        {
          byte code;
          if(i+1 < x) code = 0;
          else if(i+1 <= midxy) code = 1;
          else code = 2;
          for(int j = i+1; j < n; j++)
          {
            int dist = 0;
            switch(code)
            {
              case 0:
                if(j+1 <= midxy + 1) dist = j - i;
                else if(j+1 <= y) dist = x - (i + 1) + 1 + y - (j + 1);
                else dist = x - (i + 1) + 1 + (j + 1) - y;
                break;
                
              case 1:
                if(j+1 <= midxy + 1) dist = j - i;
                else if(j+1 <= y)
                {
                  int d1 = j - i;
                  int d2 = y - x + 1 - d1;
                  dist = d1 < d2 ? d1 : d2;
                }
                else dist = (i+1) - x + 1 + (j+1) - y;
                break;
                
              case 2:
                dist = j - i;
                break;              
            }
            
            //Console.WriteLine(dist);
            cnt[dist-1] = cnt[dist-1] + 1;
          }
        }
      
        foreach(int ans in cnt) Console.WriteLine(ans);

	}
}