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.Collections.Generic;

namespace _20200328
{
    class Program
    {
        static void Main()
        {
            var firstLine = Console.ReadLine().Split(' ');
            var n = int.Parse(firstLine[0]);
            var x = int.Parse(firstLine[1]) - 1;
            var y = int.Parse(firstLine[2]) - 1;
            var kList = new List<int>();
            for (var ptr = 0; ptr < n; ++ptr)
            {
                kList.Add(0);
            }
            for (var i = 0; i < n - 1; ++i)
            {
                for (var j = i + 1; j < n; ++j)
                {
                    //Console.WriteLine("({0}, {1}) {2}", i+1, j+1, CalcDistance(x, y, i, j));
                    ++kList[CalcDistance(x, y, i, j)];
                }
            }
            for (var ptr = 1; ptr < n; ++ptr)
            {
                Console.WriteLine(kList[ptr]);
            }
        }
        static int CalcDistance(int x, int y, int i, int j)
        {
            int under = int.MaxValue;
            if (i <= x && y <= j)
            {
                return j - i - y + x + 1;
            }
            if (i <= x && x < j && j < y)
            {
                under = x - i + 1 + y - j;
            }
            else if (x < i && j < y)
            {
                under = i - x + 1 + y - j;
            }
            else if (x < i && i < y && y <= j)
            {
                under = i - x + 1 + j - y;
            }
            return (under < j - i) ? under : j - i;
        }
    }
}