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.Generic;
using System.IO;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);

        var N = sc.ReadInt();
        var X = sc.ReadInt() - 1;
        var Y = sc.ReadInt() - 1;
        var dij = new Dijkstra(N);
        dij.Add(X, Y);
        for (int i = 0; i < N - 1; i++)
        {
            dij.Add(i, i + 1);
        }
        var ans = new int[N];
        for (int i = 0; i < N; i++)
        {
            var dp = dij.Calc(i);
            for (int j = i + 1; j < N; j++)
            {
                ans[dp[j]]++;
            }
        }
        for (int i = 1; i < N-1; i++)
        {
            Console.WriteLine(ans[i]);
        }

        Console.Out.Flush();
    }

    class Dijkstra
    {
        public int V { get; set; }
        public int E { get; set; }
        public List<Edge>[] G { get; set; }
        public bool Directed { get; set; }
        public Dijkstra(int n, bool directed = false)
        {
            this.V = n;
            this.Directed = directed;
            this.G = new List<Edge>[V];
            for (int i = 0; i < V; i++)
            {
                this.G[i] = new List<Edge>();
            }
        }
        public void Add(int a, int b, long cost = 1)
        {
            this.G[a].Add(new Edge(b, cost));
            if (!this.Directed) this.G[b].Add(new Edge(a, cost));
            this.E++;
        }
        public long GetMinCost(int start, int goal)
        {
            var cost = new long[V];
            for (int i = 0; i < V; i++) cost[i] = long.MaxValue;
            cost[start] = 0;

            var capacity = Math.Max(1, E);
            var q = new PriorityQueue<P>(capacity, false);
            q.Enqueue(new P(start, 0));

            while (q.Count > 0)
            {
                var p = q.Dequeue();
                if (p.Cost != cost[p.A]) continue;
                foreach (var e in this.G[p.A])
                {
                    if (cost[e.To] > p.Cost + e.Cost)
                    {
                        cost[e.To] = p.Cost + e.Cost;
                        q.Enqueue(new P(e.To, cost[e.To]));
                    }
                }
            }
            return cost[goal] == long.MaxValue ? -1 : cost[goal];
        }
        public long[] Calc(int start)
        {
            var cost = new long[V];
            for (int i = 0; i < V; i++) cost[i] = long.MaxValue;
            cost[start] = 0;

            var capacity = Math.Max(1, E);
            var q = new PriorityQueue<P>(capacity, false);
            q.Enqueue(new P(start, 0));

            while (q.Count > 0)
            {
                var p = q.Dequeue();
                if (p.Cost != cost[p.A]) continue;
                foreach (var e in this.G[p.A])
                {
                    if (cost[e.To] > p.Cost + e.Cost)
                    {
                        cost[e.To] = p.Cost + e.Cost;
                        q.Enqueue(new P(e.To, cost[e.To]));
                    }
                }
            }
            return cost;
        }
        public struct Edge
        {
            public int To;
            public long Cost;
            public Edge(int to, long cost)
            {
                this.To = to;
                this.Cost = cost;
            }
        }
        public struct P : IComparable<P>
        {
            public int A;
            public long Cost;
            public P(int a, long cost)
            {
                this.A = a;
                this.Cost = cost;
            }
            public int CompareTo(P other)
            {
                return this.Cost.CompareTo(other.Cost);
            }
        }
    }
    class PriorityQueue<T>
    {
        public readonly T[] Array;
        public readonly bool Greater;
        public int Count { get; private set; } = 0;
        private IComparer<T> Cmp;
        public PriorityQueue(int capacity, bool greater = true, IComparer<T> cmp = null)
        {
            this.Cmp = cmp;
            if (cmp == null)
            {
                this.Cmp = Comparer<T>.Default;
            }
            this.Array = new T[capacity];
            this.Greater = greater;
        }
        public void Enqueue(T item)
        {
            this.Array[this.Count] = item;
            this.Count += 1;
            this.UpHeap();
        }
        public T Dequeue()
        {
            this.Swap(0, this.Count - 1);
            this.Count -= 1;
            this.DownHeap();

            return this.Array[this.Count];
        }
        public T Peek()
        {
            return this.Array[0];
        }
        private void UpHeap()
        {
            var n = this.Count - 1;
            while (n != 0)
            {
                var parent = (n - 1) / 2;

                if (this.Compare(this.Array[n], this.Array[parent]) > 0)
                {
                    this.Swap(n, parent);
                    n = parent;
                }
                else
                {
                    break;
                }
            }
        }
        private void DownHeap()
        {
            var parent = 0;
            while (true)
            {
                var child = 2 * parent + 1;
                if (child > this.Count - 1) break;

                if (child < this.Count - 1 && this.Compare(this.Array[child], this.Array[child + 1]) < 0)
                {
                    child += 1;
                }
                if (this.Compare(this.Array[parent], this.Array[child]) < 0)
                {
                    this.Swap(parent, child);
                    parent = child;
                }
                else
                {
                    break;
                }
            }
        }
        private int Compare(T a, T b)
        {
            var c = this.Cmp.Compare(a, b);
            if (!this.Greater)
            {
                c = -c;
            }
            return c;
        }
        private void Swap(int a, int b)
        {
            var tmp = this.Array[a];
            this.Array[a] = this.Array[b];
            this.Array[b] = tmp;
        }
    }
    static Scanner sc = new Scanner();
}

class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }
    public string ReadStr()
    {
        return this.Next();
    }
    public char ReadChar()
    {
        return this.Next()[0];
    }
    public int ReadInt()
    {
        return int.Parse(this.Next());
    }
    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }
    public long ReadLong()
    {
        return long.Parse(this.Next());
    }
    public double ReadDouble()
    {
        return double.Parse(this.Next());
    }
    public Tuple<int, int> ReadTup(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<long, long> ReadTupLong(int add = 0)
    {
        return Tuple.Create(this.ReadLong() + add, this.ReadLong() + add);
    }
    public Tuple<int, int, int> ReadTup3(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<int, int, int, int> ReadTup4(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }
    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }
    public double[] ReadDoubleArray(int n)
    {
        var array = new double[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadDouble();
        }
        return array;
    }
    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }
    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
    public Tuple<long, long>[] ReadTupLongArray(int n, int add = 0)
    {
        var array = new Tuple<long, long>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTupLong(add);
        }
        return array;
    }
    public Tuple<int, int>[] ReadTupArray(int n, int add = 0)
    {
        var array = new Tuple<int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup(add);
        }
        return array;
    }
    public Tuple<int, int, int>[] ReadTup3Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup3(add);
        }
        return array;
    }
    public Tuple<int, int, int, int>[] ReadTup4Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup4(add);
        }
        return array;
    }
}