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)

fun main() {
    val n = nextInt()
    val x = nextInt() - 1
    val y = nextInt() - 1
    val result = IntArray(n)

    for (i in 0 until n-1) {
        for (j in i+1 until n) {
            val d = Math.min(j-i, Math.abs(x - i) + Math.abs(y - j) + 1)
            result[d]++
        }
    }

    for (i in 1 until n) {
        println(result[i])
    }
}

val scanner = java.util.Scanner(System.`in`)
fun next(): String = scanner.next()
fun nextInt() = scanner.nextInt()
fun nextLong() = scanner.nextLong()
fun nextLine() = scanner.nextLine()
fun nextList() = scanner.nextLine().split(" ")
fun nextIntList() = nextList().map(String::toInt)
fun nextLongList() = nextList().map(String::toLong)
fun printYesNo(isYes: Boolean) = println(if (isYes) "Yes" else "No")

fun main(args: Array<String>) = main()