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: Wrong Answer)

using System;

class program {
	public static void Main(string[] args){
      var nxy=Console.ReadLine().Split(' ');
      var n=int.Parse(nxy[0]);
      var x=int.Parse(nxy[1]);
      var y=int.Parse(nxy[2]);
      for(var k=1;k<n;k++){
        var kk=k-1;
        var p=Math.Max(Math.Max(n-y,0)+Math.Max(x-1,0)+1-(kk), 0);

	      if ((y-x) > k) {
				p+=Math.Max(Math.Min(y+kk,n)-Math.Max(x-kk,1)-kk, 0);
			}else{
				p+=Math.Max((y-1)-Math.Max(x-kk,1)-kk, 0);
				p+=Math.Max(Math.Min(y+kk,n)-(x+1)-kk, 0);
			}
      	Console.WriteLine(p);
      }
    }
}