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.Collections;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Globalization;
using System.Diagnostics;


class Solve
{
  public Solve() { }
  public static int Main()
  {
    new Solve().calc();
    return 0;
  }


  Scanner cin;

  void calc()
  {
    cin = new Scanner();
    int N = cin.nextInt();
    int X = cin.nextInt();
    int Y = cin.nextInt();
    Console.WriteLine(N.ToString());
    for (int i=1; i<N-1; i++)
    {
      int k = i + 1;
      int first = N - (Y - X) - 1;
      int second = N - k;
      int duplicated = nCm(N - k, k - (Y - X) - 1);
      int result = first + second - duplicated;
      Console.WriteLine(result.ToString());
    }
  }
  int nCm(int n, int m)
  {
    if (m == 0) return 1;
    if (n == 0) return 0;
    return n * nCm(n - 1, m - 1) / m;
  }
}
class Modulo
{
  private const int M = 1000000007;
  private readonly int[] m_facs;
  public int Mul(int a, int b)
  {
    return (int)(Math.BigMul(a, b) % M);
  }
  public Modulo(int n)
  {
    m_facs = new int[n + 1];
    m_facs[0] = 1;
    for (int i = 1; i <= n; ++i)
    {
      m_facs[i] = Mul(m_facs[i - 1], i);
    }
  }
  public int Fac(int n)
  {
    return m_facs[n];
  }
  public int Pow(int a, int m)
  {
    switch (m)
    {
      case 0:
        return 1;
      case 1:
        return a;
      default:
        int p1 = Pow(a, m / 2);
        int p2 = Mul(p1, p1);
        return ((m % 2) == 0) ? p2 : Mul(p2, a);
    }
  }
  public int Div(int a, int b)
  {
    return Mul(a, Pow(b, M - 2));
  }
  public int Ncr(int n, int r)
  {
    if (n < r) { return 0; }
    if (n == r) { return 1; }
    int res = Fac(n);
    res = Div(res, Fac(r));
    res = Div(res, Fac(n - r));
    return res;
  }
}

class Scanner
{
  string[] s;
  int i;

  char[] cs = new char[] { ' ' };

  public Scanner()
  {
    s = new string[0];
    i = 0;
  }

  public string next()
  {
    if (i < s.Length) return s[i++];
    string st = Console.ReadLine();
    while (st == "") st = Console.ReadLine();
    s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
    if (s.Length == 0) return next();
    i = 0;
    return s[i++];
  }

  public int nextInt()
  {
    return int.Parse(next());
  }
  public uint nextUInt()
  {
    return uint.Parse(next());
  }
  public int[] ArrayInt(int N, int add = 0)
  {
    int[] Array = new int[N];
    for (int i = 0; i < N; i++)
    {
      Array[i] = nextInt() + add;
    }
    return Array;
  }

  public long nextLong()
  {
    return long.Parse(next());
  }

  public ulong nextULong()
  {
    return ulong.Parse(next());
  }

  public long[] ArrayLong(int N, long add = 0)
  {
    long[] Array = new long[N];
    for (int i = 0; i < N; i++)
    {
      Array[i] = nextLong() + add;
    }
    return Array;
  }

  public double nextDouble()
  {
    return double.Parse(next());
  }


  public double[] ArrayDouble(int N, double add = 0)
  {
    double[] Array = new double[N];
    for (int i = 0; i < N; i++)
    {
      Array[i] = nextDouble() + add;
    }
    return Array;
  }
}