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(args: Array<String>) {
    val (n, x, y) = readLine()!!.split(' ').map(String::toInt)
    val ansMap = Array(n + 1) { IntArray(n + 1) { 0 } }
    for (i in 1..n) {
        for (j in 1..n) {
            ansMap[i][j] = Math.abs(i - j)
        }
    }
    ansMap[x][y] = 1
    ansMap[y][x] = 1
    for (i in 1..n) {
        for (j in 1..n) {
            ansMap[i][j] = Math.min(ansMap[i][j], ansMap[i][x] + ansMap[y][j] + 1)
            ansMap[i][j] = Math.min(ansMap[i][j], ansMap[i][y] + ansMap[x][j] + 1)
        }
    }
    val ansArray = IntArray(n) { 0 }
    for (i in 1..n) {
        for (j in 1..n) {
            ansArray[ansMap[i][j]]++
        }
    }
    for (k in 1 until n) {
        println(ansArray[k] / 2)
    }
}