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;
using System.IO;
using System.Linq;
using System.Reflection;
using System.Text;

namespace A
{
    class StartingPoint
    {
        static void Main(string[] args)
        {
            if (args?.Any() == true)
            {
                var assembly = Assembly.GetEntryAssembly();
                var resourceName = "AtCoderCSharp.In.txt";
                var stream = assembly.GetManifestResourceStream(resourceName);
                var streamReader = new StreamReader(stream, Encoding.UTF8);
                var str = streamReader.ReadToEnd();
                var textReader = new StringReader(str);
                Console.SetIn(textReader);
            }

            try
            {
                foreach (var s in new Program().Solve())
                {
                    Console.WriteLine(s);
                }
            }
            catch (Exception e)
            {
                Console.WriteLine(e);
                if (args?.Any() != true)
                    throw e;
            }

            if (args?.Any() == true)
                Console.ReadKey();
        }
    }

    class Program
    {
        public List<int> ScanInts(int count) => Enumerable.Range(0, count).Select(_ => ScanInt).ToList();
        public List<int> ScanInts(long count) => ScanInts((int)count);
        public List<long> ScanLongs(int count) => Enumerable.Range(0, count).Select(_ => Scan).ToList();
        public List<long> ScanLongs(long count) => ScanLongs((int)count);
        public int ScanInt => int.Parse(Str);
        public long Scan => long.Parse(Str);
        public double ScanDouble => (double)Scan;

        StringBuilder sb = new StringBuilder();

        public string Str => ScanStr();
        public string ScanStr()
        {
            sb.Clear();

            int r = 0;
            bool? b = null;
            do
            {
                r = Console.Read();
                b = IsBreak(r);
            } while (b == true);

            if (b == null)
                throw new Exception("input error: unexpected end of stream");

            do
            {
                sb.Append((char)r);
                r = Console.Read();
                b = IsBreak(r);
            } while (b == false);

            return sb.ToString();
        }

        bool? IsBreak(int c)
        {
            switch (c)
            {
                case -1:
                    return null;
                case (int)' ':
                case (int)'\n':
                case (int)'\r':
                    return true;
                default:
                    return false;
            }
        }

        public IEnumerable<int> Loop(int count) => Enumerable.Range(0, count);
        public IEnumerable<int> Loop(int from, int to) => Enumerable.Range(from, to - from + 1);

        public IEnumerable<long> Loop(long count) => Loop(0, count - 1);
        public IEnumerable<long> Loop(long from, long to)
        {
            for (long i = from; i <= to; i++)
                yield return i;
        }

        public string YesNo(bool isYes) => isYes ? "Yes" : "No";

        public HashSet<T> ToHashSet<T>(IEnumerable<T> ts) => new HashSet<T>(ts);


        struct Mint
        {
            public static long Divider { set { divider = value; } }
            private static long divider = 1000000007;
            public static void Set998244353() { divider = 998244353; }

            public long Value { get; }

            public Mint(long value)
            {
                this.Value = value;
            }

            public static Mint operator +(Mint a, Mint b) => new Mint((a.Value + b.Value) % divider);

            public static Mint operator -(Mint a, Mint b)
            {
                var t = (a.Value - b.Value) % divider;
                if (t < 0)
                    t += divider;
                return new Mint(t);
            }

            public static Mint operator *(Mint a, Mint b) => new Mint((a.Value * b.Value) % divider);

            public static Mint operator /(Mint a, Mint b) => new Mint((a.Value * InvImpl(b.Value)) % divider);

            public Mint Pow(long p) => new Mint(PowImpl(Value, p));
            private static long PowImpl(long a, long p)
            {
                if (p == 0)
                    return 1L;

                if (p == 1)
                    return a;

                var halfP = p / 2;
                var halfPowered = PowImpl(a, halfP);
                var powered = halfPowered * halfPowered % divider;
                return p % 2 == 0 ? powered : powered * a % divider;
            }

            public static Mint Inv(long a) => new Mint(InvImpl(a));
            private static readonly Dictionary<long, long> invCache = new Dictionary<long, long>();
            private static long InvImpl(long a)
            {
                long cache = 0L;
                if (invCache.TryGetValue(a, out cache))
                    return cache;

                var result = PowImpl(a, divider - 2);
                invCache.Add(a, result);
                return result;
            }

            public static Mint Fac(long a) => new Mint(FacImpl(a));
            private static readonly List<long> facCache = new List<long>() { 1L };
            private static long FacImpl(long a)
            {
                if (a >= divider)
                    return 0;

                var val = 1L;
                var start = 1;
                for (int i = start; i <= a; i++)
                {
                    val = (val * i) % divider;
                }

                return val;
            }

            public static Mint Perm(long n, long r) => new Mint(PermImpl(n, r));
            private static long PermImpl(long n, long r)
            {
                if (n < r)
                    return 0L;

                if (r <= 0)
                    return 1L;

                var nn = FacImpl(n);
                var nr = FacImpl(n - r);
                return (nn * InvImpl(nr)) % divider;
            }

            public static Mint Comb(long n, long r) => new Mint(CombImpl(n, r));
            private static long CombImpl(long n, long r)
            {
                if (n < r)
                    return 0L;

                if (n == r)
                    return 1L;

                if (n - r < r)
                    return CombImpl(n, n - r);

                var nr = 1L;
                for (var i = n; i > n - r; i--)
                {
                    nr *= i;
                    nr %= divider;
                }
                var rr = FacImpl(r);

                return (nr * InvImpl(rr)) % divider;
            }
        }


        public IEnumerable<string> Solve()
        {
            var n = ScanInt;
            var x = ScanInt - 1;
            var y = ScanInt - 1;

            var res = Enumerable.Range(0, n - 1).Select(_ => 0).ToList();

            for (int i = 0; i < n; i++)
            {
                for (int j = i + 1; j < n; j++)
                {
                    var d = j - i;
                    d = Math.Min(d, Math.Abs(i - x) + 1 + Math.Abs(j - y));
                    d = Math.Min(d, Math.Abs(i - y) + 1 + Math.Abs(j - x));
                    res[d - 1]++;
                }
            }

            return res.Select(a => a.ToString());
        }
    }
}