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;
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 xside = x - 1;
            int yside = n - y;
            int ring = y - x + 1;
            int half = ring / 2;

            Console.WriteLine(n);

            bool isEvenRing = ring % 2 == 0;
            for (int d = 2; d < n; d++)
            {
                int xn = Line(xside, d);
                int yn = Line(yside, d);
                int hn = Line(half, d);
                int rn = ring > d * 2 ? ring :
                         ring == d * 2 ? d : 0;
                int count = xn + yn + rn;

                count += 2 * (Line(xside + half, d) - xn - hn);
                count += 2 * (Line(yside + half, d) - yn - hn);
                if (isEvenRing && d > half)
                {
                    int diff = d - half;
                    if (diff <= xside)
                        count--;
                    if (diff <= yside)
                        count--;
                }
                if (xside > 0 && yside > 0)
                    count += Line(xside + yside + 1, d) - Line(xside + 1, d) - Line(yside + 1, d);
                Console.WriteLine(count);
            }
        }

        public static int Line(int length, int distance)
        {
            int t = length - distance + 1;
            return t > 0 ? t : 0;
        }
    }
}