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: Time Limit Exceeded)

import java.io.PrintWriter
import java.util.*

fun main(args: Array<String>) {
    PrintWriter(System.out).use { out ->
        solve(out)
        out.flush()
    }
}

fun solve(out: PrintWriter) {
//    val (n, x, y) = readIntegerList()
//    val INF = Int.MAX_VALUE
//    val map = IntArray(n) { INF }
//    val queue = ArrayDeque<Int>()
//    map[0] = 0
//    queue.addLast(0)
//    while (queue.isNotEmpty()) {
//        val p = queue.removeFirst()
//
//        if (p + 1 in (0 until n) && map[p + 1] == INF) {
//            map[p + 1] = map[p] + 1
//            queue.addLast(p + 1)
//        }
//
//        if (p - 1 in (0 until n) && map[p - 1] == INF) {
//            map[p - 1] = map[p] + 1
//            queue.addLast(p - 1)
//        }
//
//        if (p == x - 1 && map[y - 1] == INF) {
//            map[y - 1] = map[p] + 1
//            queue.addLast(y - 1)
//        }
//    }
//
//    println(map.joinToString(" "))
//    val ans = IntArray(n - 1)
//    for (i in 0 until n) {
//        println("-------" + i)
//        for (j in (i + 1) until n) {
//            var d = map[j] - map[i] - 1
//            if (d in 0 until (n - 1)) ans[d]++
//
//            d = map[i] - map[j] - 1
//            if (d in 1 until (n - 1)) ans[d]++
//            println(ans.joinToString(" "))
//        }
//        println()
//    }
//    println(ans.joinToString("\n"))

    val (n, x, y) = readIntegerList()
    val INF = Long.MAX_VALUE
    val map = Array(n) { LongArray(n) { INF } }
    for (i in 0 until (n - 1)) {
        map[i][i + 1] = 1
        map[i + 1][i] = 1
    }
    map[x - 1][y - 1] = 1
    map[y - 1][x - 1] = 1
    warshallFloyd(map)
//    for (i in 0 until n) {
//        println(map[i].joinToString(" "))
//    }

    val ans = LongArray(n - 1)
    for (i in 0 until n) {
        for (j in (i + 1) until n) {
            ans[(map[i][j] - 1).toInt()]++
        }
    }
    println(ans.joinToString("\n"))
}

fun warshallFloyd(costMatrix: Array<LongArray>) {
    val indices = costMatrix.indices
    for (k in indices)
        for (i in indices)
            for (j in indices)
                if (costMatrix[i][k] != Long.MAX_VALUE && costMatrix[k][j] != Long.MAX_VALUE)
                    costMatrix[i][j] = Math.min(costMatrix[i][j], costMatrix[i][k] + costMatrix[k][j])
}

fun readInteger() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntegerList() = readStringList().map(String::toInt)
fun readLongList() = readStringList().map(String::toLong)
fun readDoubleList() = readStringList().map(String::toDouble)