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 (1.0.0) (judge verdict: Accepted)

import java.io.BufferedReader
import java.io.InputStream
import java.io.InputStreamReader
import java.io.PrintWriter
import java.lang.StringBuilder
import java.util.*

fun PrintWriter.solve(sc: FastScanner) {
    val n = sc.nextInt()
    val x = sc.nextInt() - 1
    val y = sc.nextInt() - 1
    var ans = Array(n - 1) { 0 }
    for (i in 0 until n) {
        val dist = Array(n) { 0 }
        val visited = Array(n) { false }
        visited[i] = true
        val que = ArrayDeque<Pair<Int, Int>>()
        que.add(i to 0)
        while (que.count() > 0) {
            val (v, step) = que.pollFirst()
            dist[v] = step
            if (v > 0 && !visited[v - 1]) {
                visited[v - 1] = true
                que.add(v - 1 to step + 1)
            }
            if (v < n - 1 && !visited[v + 1]) {
                visited[v + 1] = true
                que.add(v + 1 to step + 1)
            }
            if (v == x && !visited[y]) {
                visited[y] = true
                que.add(y to step + 1)
            }
            if (v == y && !visited[x]) {
                visited[x] = true
                que.add(x to step + 1)
            }
        }
        for (j in 0 until n) {
            if (dist[j] != 0) {
                ans[dist[j] - 1]++
            }
        }
    }
    println(ans.map { it / 2 }.joinToString("\n"))
}

fun main(args: Array<String>) {
    val writer = PrintWriter(System.out, false)
    writer.solve(FastScanner(System.`in`))
    writer.flush()
}

class FastScanner(s: InputStream) {
    private var st = StringTokenizer("")
    private val br = BufferedReader(InputStreamReader(s))

    fun next(): String {
        while (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())

        return st.nextToken()
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextLine() = br.readLine()
    fun nextDouble() = next().toDouble()
    fun ready() = br.ready()
}