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;

namespace ABC160D
{
    class Program
    {
        static void Main(string[] args)
        {
            var NXY = ReadInt();
            int N = NXY[0];
            int X = NXY[1] - 1;
            int Y = NXY[2] - 1;

            int[] s = new int[N];
            int[] t = new int[N];
            for (int i = 0; i < N - 1; i++)
            {
                s[i] = i; t[i] = i + 1;
            }
            s[N - 1] = X;
            t[N - 1] = Y;

            int[] ans = new int[N];
            for (int i = 0; i < N; i++)
            {
                int[] d = new int[N];
                for (int j = 0; j < N; j++)
                {
                    d[j] = int.MaxValue / 2;
                }
                d[i] = 0;

                Queue<edge> que = new Queue<edge>();
                que.Enqueue(new edge() { point = i, cost = 0 });

                while (que.Count > 0)
                {
                    edge now = que.Dequeue();
                    if (now.cost > d[now.point]) continue;
                    d[now.point] = now.cost;

                    int next = now.point + 1;
                    int prev = now.point - 1;
                    int edge = -1;
                    if (now.point == X) edge = Y;
                    else if (now.point == Y) edge = X;

                    if (next < N) que.Enqueue(new edge() { point = next, cost = now.cost + 1 });
                    if (prev >= 0) que.Enqueue(new edge() { point = prev, cost = now.cost + 1 });
                    if (edge != -1) que.Enqueue(new edge() { point = edge, cost = now.cost + 1 });
                }

                for (int j = 0; j < N; j++)
                {
                    ans[d[j]]++;
                }
            }

            for (int i = 1; i < N; i++)
            {
                Console.WriteLine(ans[i] / 2);
            }

            Console.ReadKey();
        }

        struct edge
        {
            public int point;
            public int cost;
        }

        static int[] ReadInt()
        {
            int[] ret = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return ret;
        }
        static long[] ReadLong()
        {
            long[] ret = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return ret;
        }
    }
}