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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.PrintWriter
import java.util.*
import kotlin.math.min

fun main() {
    val reader = System.`in`.bufferedReader()
    val writer = PrintWriter(System.out, false)

    var tokenizer: StringTokenizer = StringTokenizer("")

    fun next(): String {
        while (tokenizer.hasMoreTokens().not()) tokenizer = StringTokenizer(reader.readLine())
        return tokenizer.nextToken()
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextDouble() = next().toDouble()
    fun nextLine() = reader.readLine()

    fun PrintWriter.solve() {
        var (n,x,y) = List(3){nextInt()}
        var graph = Array(n){ mutableListOf<Int>()}

        for (i in 0..n-2){
            graph[i].add(i+1)
            graph[i+1].add(i)
        }

        graph[x-1].add(y-1)
        graph[y-1].add(x-1)

//        println(Arrays.toString(graph))
        var map = mutableMapOf<Int,Int>()
        val mxn = 1_000_000

        for (cur in 0..n-1){
            var q = ArrayDeque<Pair<Int,Int>>()
            var dist = IntArray(n){-1}
            dist[cur] = 0

            graph[cur].forEach { q.add(Pair(it,1)) }

            while (q.isEmpty().not()){
//                println(q)
                var pop = q.pollFirst()
                var u = pop.first
                var d = pop.second
                if (dist[u] != -1)continue

                dist[u] = d

                graph[u].filter { dist[it] == -1 }.forEach { q.add(Pair(it,d+1)) }
            }

//            println(Arrays.toString(dist))
            for (d in dist){
                map[d] = map.getOrDefault(d,0) + 1
            }


//            println(Arrays.toString(dist))

        }



        for (i in 1..n-1){
            println(map.getOrDefault(i,0)/2)
        }







    }

    writer.solve()
    writer.flush()


}