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;
using System.Linq;

namespace AtCoder
{
    class Abc160D
    {
        public static void Main()
        {
            var nxy = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            int n = nxy[0];
            int x = nxy[1];
            int y = nxy[2];

            // y-x+1のringと1:x , y:Nを考える

            int foot = n - y;
            int head = x - 1;

            int ring = y - x + 1;
            int line = x + n - y;

            Console.WriteLine(n);

            for (int d = 2; d < n; d++)
            {
                int count = 0;
                int d2 = d * 2;
                if (ring >= d2)
                    count += ring;
                if (line >= d)
                    count += line - d + 1;

                if (head >= d - 1)
                    count++;
                if (foot >= d - 1)
                    count++;

                for (int k = 2; k < d; k++)
                {
                    int k2 = k * 2;
                    if (ring < k2)
                        break;
                    int c = ring == k2 ? 1 : 2;

                    int temp = 0;
                    if (head >= d - k)
                        temp += c;
                    if (foot >= d - k)
                        temp += c;
                    if (temp == 0)
                        break;
                    count += temp;
                }
                Console.WriteLine(count);
            }
        }
    }
}