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: Time Limit Exceeded)

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

class Program
{
    const string Yes = "Yes";
    const string No = "No";
    const long Mod = 1000000007;
    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
        //MyDebugger.Test(process, "../TextFile2.txt");
        //MyDebugger.MakeTestCase("../TextFile2.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }
    static int n;
    static int x;
    static int y;
    static int[][] tbl;

    static object process(TextReader input) {
        var spl = input.ReadLine().Split(' ');
        n = int.Parse(spl[0]);
        x = int.Parse(spl[1])-1;
        y = int.Parse(spl[2])-1;

        tbl = new int[n][];
        var tblX = new int[n][];
        for (int i = 0; i < n; i++) {
            tbl[i] = new int[n];
            tblX[i] = new int[n];
            for(int j=0; j<n; j++) {
                tbl[i][j] = 9999;
            }
        }

        while (true) {
            bool quit = true;
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i == j) {
                        tbl[i][j] = 0;
                    } else {
                        int z = tbl[i][j];
                        if (j > 0)     z = Math.Min(z, tbl[i][j - 1] + 1);
                        if (j < n - 1) z = Math.Min(z, tbl[i][j + 1] + 1);
                        if (j == y)    z = Math.Min(z, tbl[i][x] + 1);
                        if (j == x)    z = Math.Min(z, tbl[i][j] + 1);
                        if(z < tbl[i][j]) {
                            tbl[i][j] = z;
                            quit = false;
                        }
                    }
                }
            }
            if (quit) break;
        }

        var counts = new int[10010];

        for(int i=0; i<n; i++) {
            for (int j = i + 1; j < n; j++) {
                int z = min(tbl[i][j], tbl[j][i]);
                tblX[i][j] = z;
                counts[z]++;
            }
        }

        var bu = new StringBuilder();
        for(int i=1; i<=n-1; i++) {
            bu.AppendLine(counts[i].ToString());
        }

        return bu;
    }

    static int min(int x, int y) {
        if (x == 0) return y;
        if (y == 0) return x;
        return Math.Min(x, y);
    }
}