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.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val n = sc.nextInt()
    val x = sc.nextInt()
    val y = sc.nextInt()
    println(problem160d(n, x, y))
}

fun problem160d(n: Int, x: Int, y: Int): String {
    val dist = Array(n) { IntArray(n) { -1 } }
    for (s in 0 until n) {
        val que = ArrayDeque<Int>()
        que.offer(s)
        dist[s][s] = 0
        while (!que.isEmpty()) {
            val v = que.poll()
            val nvs = mutableListOf<Int>()
            if (v > 0) nvs.add(v - 1)
            if (v < n - 1) nvs.add(v + 1)
            if (v == x - 1) nvs.add(y - 1)
            if (v == y - 1) nvs.add(x - 1)
            for (nv in nvs) {
                if (dist[s][nv] == -1) {
                    dist[s][nv] = dist[s][v] + 1
                    que.offer(nv)
                }
            }
        }
    }
    val res = IntArray(n) { 0 }
    for (i in 0 until n) {
        for (j in i + 1 until n) {
            res[dist[i][j]]++
        }
    }
    return res.drop(1).joinToString("\n")
}