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.Linq;
using System.IO;
using System.Text;
using System.Threading.Tasks;
using System.Globalization;
using System.Collections;

namespace Atcoder2
{
    class Program
    {
        static void Main(string[] args)
        {
            StreamScanner scan = new StreamScanner(System.Console.OpenStandardInput());
            int n = scan.Integer();
            int x = scan.Integer()-1;
            int y = scan.Integer()-1;
            int[,] kyori = new int[n, n];
            int[] kyoris = new int[n];
            for (int i = 0; i < n; i++)
            {
                int maekyori = Math.Min(Math.Abs(x - i), Math.Abs(y - i));
                for (int k = i; k < n; k++)
                {
                    int atokyori = Math.Min(Math.Abs(x - k), Math.Abs(y - k));
                    kyori[i, k] = Math.Min(maekyori + atokyori + 1, k - i);
                    kyoris[kyori[i, k]]++;
                }
            }
            for (int i = 1; i < n; i++)
            {
                Console.WriteLine(kyoris[i]);
            }
        }
        static int[] zalgo(String s)
        {
            int n = s.Length;
            int[] ret = new int[n];
            ret[0] = n;
            int i = 1, j = 0;
            while (i < n)
            {
                while (i + j < n && s[j] == s[i + j])
                    ++j;
                ret[i] = j;
                if (j == 0)
                {
                    ++i;
                    continue;
                }
                int k = 1;
                while (i + k < n && k + ret[k] < j)
                {
                    ret[i + k] = ret[k];
                    ++k;
                }
                i += k;
                j -= k;
            }
            return ret;
        }
        static int gcd(int a, int b)
        {
            if (a % b == 0) { return b; }
            return gcd(b, a % b);
        }
        static int[] yousogotoplus(int[] a, int[] b)
        {
            int[] c = new int[a.Length];
            for (int i = 0; i < a.Length; i++)
            {
                c[i] = a[i] + b[i];
            }
            return c;
        }
        static int[] yousogotoplus(int[] a, int[,] b, int l)
        {
            int[] c = new int[a.Length];
            for (int i = 0; i < a.Length; i++)
            {
                c[i] = a[i] + b[l, i];
            }
            return c;
        }

        static int[] yousogotoplus(int[,] a, int l)
        {
            int[] c = new int[a.GetLength(1)];
            for (int i = 0; i < a.GetLength(1); i++)
            {
                c[i] = a[l, i];
            }
            return c;
        }
        static long solve(int mae, int ushiro, long[,] dp, int[] a, bool taro)
        {
            if (dp[mae, ushiro] > long.MinValue)
            {
                return dp[mae, ushiro];
            }
            if (ushiro - mae == 1)
            {
                if (taro) { dp[mae, ushiro] = a[mae]; return dp[mae, ushiro]; }
                else { dp[mae, ushiro] = -a[mae]; return dp[mae, ushiro]; }
            }

            if (taro)
            {
                long max = Math.Max(a[mae] + solve(mae + 1, ushiro, dp, a, !taro),
                    a[ushiro - 1] + solve(mae, ushiro - 1, dp, a, !taro));
                dp[mae, ushiro] = max;
                return dp[mae, ushiro];

            }
            else
            {
                long min = Math.Min(-a[mae] + solve(mae + 1, ushiro, dp, a, !taro),
                    -a[ushiro - 1] + solve(mae, ushiro - 1, dp, a, !taro));
                dp[mae, ushiro] = min;
                return dp[mae, ushiro];
            }

        }

        static int nibutan(int med, int[] a)//med以上が何個あるか
        {
            int mae = 0;
            int ato = a.Length;
            while (true)
            {
                if (ato - mae <= 1)
                {
                    return mae;
                }
                int mid = (mae + ato) / 2;
                if (a[mid] > med) { ato = mid; }
                if (a[mid] <= med) { mae = mid; }
            }
        }
        static int binary_search(int key, int[] moto)
        {
            int ng = -1;
            int ok = moto.Length;
            while (Math.Abs(ok - ng) > 1)
            {
                int mid = (ok + ng) / 2;
                if (isOK(mid, key, moto)) { ok = mid; }
                else { ng = mid; }
            }
            return ok;
        }
        static bool isOK(int index, int key, int[] moto)
        {
            return moto[index] >= key;
        }

        public static int h;
        public static int w;
        public static int BFS(int height, int width, char[,] map)
        {
            int[] dx = new int[] { -1, 0, 0, 1 };
            int[] dy = new int[] { 0, 1, -1, 0 };
            bool[,] visited = new bool[h, w];
            int[,] len = new int[h, w];
            var queue = new Queue<Tuple<int, int>>();
            queue.Enqueue(new Tuple<int, int>(height, width));
            int max = 0;
            visited[height, width] = true;

            while (queue.Count > 0)
            {
                var now = queue.Dequeue();
                for (int i = 0; i < 4; i++)
                {
                    int ny = now.Item1 + dy[i];
                    int nx = now.Item2 + dx[i];
                    if (ny >= h || ny < 0 || nx >= w || nx < 0)
                        continue;
                    if (visited[ny, nx] || map[ny, nx] == '#')
                        continue;
                    visited[ny, nx] = true;
                    len[ny, nx] = len[now.Item1, now.Item2] + 1;
                    max = Math.Max(max, len[ny, nx]);
                    queue.Enqueue(new Tuple<int, int>(ny, nx));
                }
            }
            return max;
        }
    }
    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }
        private readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        private byte read()
        {
            if (isEof) throw new EndOfStreamException();
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
        public char Char()
        {
            byte b = 0;
            do b = read();
            while (b < 33 || 126 < b);
            return (char)b;
        }
        public char[] Char(int n)
        {
            char[] kore = new char[n];
            for (int i = 0; i < n; i++)
            {
                kore[i] = Char();
            }
            return kore;
        }
        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        public long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        public long[] Long(int n)
        {
            long[] kore = new long[n];
            for (int i = 0; i < n; i++)
            {
                kore[i] = Long();
            }
            return kore;
        }
        public int Integer() { return (int)Long(); }
        public int[] Integer(int n)
        {
            int[] kore = new int[n];
            for (int i = 0; i < n; i++)
            {
                kore[i] = (int)Long();
            }
            return kore;
        }
        public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
    public class UnionFind
    {
        public int[] data;

        public UnionFind(int size)
        {
            data = new int[size];
            for (int i = 0; i < size; i++) data[i] = -1;
        }

        public bool Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);

            if (x != y)
            {
                if (data[y] < data[x])
                {
                    var tmp = y;
                    y = x;
                    x = tmp;
                }
                data[x] += data[y];
                data[y] = x;
            }
            return x != y;
        }

        public bool IsSameGroup(int x, int y)
        {
            return Root(x) == Root(y);
        }

        public int Root(int x)
        {
            return data[x] < 0 ? x : data[x] = Root(data[x]);
        }
    }
    public class Mlong
    {
        private static long mod = 1000000007;
        public long num;
        public Mlong(long num) { this.num = num; }
        public override int GetHashCode()
        {
            return num.GetHashCode();
        }
        public override bool Equals(object obj)
        {
            return num.Equals(obj);
        }
        public static Mlong operator +(Mlong x, Mlong y)
        {
            return new Mlong((x.num + y.num) % mod);
        }
        public static Mlong operator -(Mlong x, Mlong y)
        {
            return new Mlong((x.num - y.num + mod) % mod);
        }
        public static Mlong operator *(Mlong x, Mlong y)
        {
            return new Mlong((long)(((1L * x.num) * y.num) % mod));
        }
        public Mlong hutujyo(Mlong x)
        {
            return new Mlong(num / x.num);
        }
        public Mlong modjyo(Mlong x)
        {
            return num * x.Pow(mod - 2);
        }
        public static implicit operator Mlong(long x)
        {
            return new Mlong(x);
        }
        public static Mlong operator %(Mlong x, Mlong y)
        {
            return new Mlong(x.num % y.num);
        }
        public static bool operator ==(Mlong x, Mlong y)
        {
            return x.num == y.num;
        }
        public static bool operator !=(Mlong x, Mlong y)
        {
            return x.num != y.num;
        }
        public static bool operator <(Mlong x, Mlong y)
        {
            return x.num < y.num;
        }
        public static bool operator >(Mlong x, Mlong y)
        {
            return x.num > y.num;
        }
        public static bool operator <=(Mlong x, Mlong y)
        {
            return x.num <= y.num;
        }
        public static bool operator >=(Mlong x, Mlong y)
        {
            return x.num >= y.num;
        }
        public Mlong Pow(Mlong n)
        {

            if (n == 1) { return this % mod; }
            if (n % 2 == 1) { return (this * Pow(n - 1)) % mod; }
            Mlong buf = Pow(n.hutujyo(2));
            return (buf * buf) % mod;
        }
        public static Mlong Pow(Mlong a, Mlong n)
        {
            return a.Pow(n);
        }
        public static Mlong Comb(Mlong n, Mlong a)
        {
            Mlong buf1 = 1;
            Mlong buf2 = 1;
            for (long i = 0; i < a; i++)
            {
                buf1 *= n - i;
                buf2 *= (i + 1);
            }
            return buf1.modjyo(buf2);

        }
        public static void WriteLine(Mlong x)
        {
            Console.WriteLine(x.num);

        }
    }
    public class Mint
    {
        private static int mod = 1000000007;
        public int num;
        public Mint(int Num) { num = Num; }
        public override int GetHashCode()
        {
            return num.GetHashCode();
        }
        public override bool Equals(object obj)
        {
            return num.Equals(obj);
        }
        public static Mint operator +(Mint x, Mint y)
        {
            return new Mint((x.num + y.num) % mod);
        }
        public static Mint operator -(Mint x, Mint y)
        {
            return new Mint((x.num - y.num + mod) % mod);
        }
        public static Mint operator *(Mint x, Mint y)
        {
            return new Mint((int)(((1L * x.num) * y.num) % mod));
        }
        public Mint hutujyo(Mint x)
        {
            return new Mint(num / x.num);
        }
        public Mint modjyo(Mint x)
        {
            return num * x.Pow(mod - 2);
        }
        public static implicit operator Mint(int x)
        {
            return new Mint(x);
        }
        public static Mint[] Toarray(int[] x)
        {
            Mint[] buf = new Mint[x.Length];
            for (int i = 0; i < x.Length; i++)
            {
                buf[i] = x[i];
            }
            return buf;
        }
        public static explicit operator int(Mint x)
        {
            return x.num;
        }
        public static Mint operator %(Mint x, Mint y)
        {
            return new Mint(x.num % y.num);
        }
        public static bool operator ==(Mint x, Mint y)
        {
            return x.num == y.num;
        }
        public static bool operator !=(Mint x, Mint y)
        {
            return x.num != y.num;
        }
        public static bool operator <(Mint x, Mint y)
        {
            return x.num < y.num;
        }
        public static bool operator >(Mint x, Mint y)
        {
            return x.num > y.num;
        }
        public static bool operator <=(Mint x, Mint y)
        {
            return x.num <= y.num;
        }
        public static bool operator >=(Mint x, Mint y)
        {
            return x.num >= y.num;
        }
        public Mint Pow(Mint n)
        {

            if (n == 1) { return this % mod; }
            if (n % 2 == 1) { return (this * Pow(n - 1)) % mod; }
            Mint buf = Pow(n.hutujyo(2));
            return (buf * buf) % mod;
        }
        public static Mint Pow(Mint a, Mint n)
        {
            return a.Pow(n);
        }
        public static Mint Comb(Mint n, Mint a)
        {
            Mint buf1 = 1;
            Mint buf2 = 1;
            for (int i = 0; i < a; i++)
            {
                buf1 *= n - i;
                buf2 *= (i + 1);
            }
            return buf1.modjyo(buf2);

        }
        public static void WriteLine(Mint x)
        {
            Console.WriteLine(x.num);

        }
    }
    public class PriorityQueue<T> : IEnumerable<T>
    {
        private readonly List<T> _data = new List<T>();
        private readonly IComparer<T> _comparer;
        private readonly bool _isDescending;

        public PriorityQueue(IComparer<T> comparer, bool isDescending = true)
        {
            _comparer = comparer;
            _isDescending = isDescending;
        }

        public PriorityQueue(Comparison<T> comparison, bool isDescending = true)
            : this(Comparer<T>.Create(comparison), isDescending)
        {
        }

        public PriorityQueue(bool isDescending = true)
            : this(Comparer<T>.Default, isDescending)
        {
        }

        public void Enqueue(T item)
        {
            _data.Add(item);
            var childIndex = _data.Count - 1;
            while (childIndex > 0)
            {
                var parentIndex = (childIndex - 1) / 2;
                if (Compare(_data[childIndex], _data[parentIndex]) >= 0)
                    break;
                Swap(childIndex, parentIndex);
                childIndex = parentIndex;
            }
        }

        public T Dequeue()
        {
            var lastIndex = _data.Count - 1;
            var firstItem = _data[0];
            _data[0] = _data[lastIndex];
            _data.RemoveAt(lastIndex--);
            var parentIndex = 0;
            while (true)
            {
                var childIndex = parentIndex * 2 + 1;
                if (childIndex > lastIndex)
                    break;
                var rightChild = childIndex + 1;
                if (rightChild <= lastIndex && Compare(_data[rightChild], _data[childIndex]) < 0)
                    childIndex = rightChild;
                if (Compare(_data[parentIndex], _data[childIndex]) <= 0)
                    break;
                Swap(parentIndex, childIndex);
                parentIndex = childIndex;
            }
            return firstItem;
        }

        public T Peek()
        {
            return _data[0];
        }

        private void Swap(int a, int b)
        {
            var tmp = _data[a];
            _data[a] = _data[b];
            _data[b] = tmp;
        }

        private int Compare(T a, T b)
        {
            return _isDescending ? _comparer.Compare(b, a) : _comparer.Compare(a, b);
        }

        public int Count => _data.Count;

        public IEnumerator<T> GetEnumerator()
        {
            return _data.GetEnumerator();
        }

        IEnumerator IEnumerable.GetEnumerator() => GetEnumerator();
    }
}