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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

var graph [][]int

func main() {
	var n, x, y int
	fmt.Scan(&n, &x, &y)
	graph = PrepareEmpty2DintArray(n, n)
	for k := 0; k < n-1; k++ {
		graph[k][k+1] = 1
		graph[k+1][k] = 1
		if k == x-1 {
			graph[k][y-1] = 1
			graph[y-1][k] = 1
		}
	}
	warshalFloyd(n)
	countMap := map[int]int{}
	for i := 0; i < n-1; i++ {
		for j := i + 1; j < n; j++ {
			countMap[graph[i][j]]++
		}
	}
	io, flush := NewIO()
	defer flush()
	for i := 1; i < n; i++ {
		io.Println(countMap[i])
	}
}

func PrepareEmptyIntArray(n int) []int {
	arr := make([]int, n)
	for i := 0; i < n; i++ {
		arr[i] = 1000
	}
	return arr
}

func PrepareEmpty2DintArray(x, y int) [][]int {
	arr := make([][]int, y)
	for i := 0; i < y; i++ {
		arr[i] = PrepareEmptyIntArray(x)
	}
	return arr
}
func warshalFloyd(n int) {
	for k := 0; k < n; k++ {
		for i := 0; i < n; i++ {
			for j := 0; j < n; j++ {
				graph[i][j] = int(math.Min(float64(graph[i][j]), float64(graph[i][k]+graph[k][j])))
			}
		}
	}
}


type IO struct {
	scanner *bufio.Scanner
	writer  *bufio.Writer
}

func NewIO() (*IO, func()) {
	io := &IO{
		scanner: newScanner(),
		writer:  newWriter(),
	}
	return io, func() { io.writer.Flush() }
}

func newScanner() *bufio.Scanner {
	s := bufio.NewScanner(os.Stdin)
	s.Buffer(make([]byte, 10000000), 10000000)
	s.Split(bufio.ScanWords)
	return s
}

func newWriter() *bufio.Writer {
	return bufio.NewWriter(os.Stdout)
}

func (io *IO) ScanBytes() []byte {
	if !io.scanner.Scan() {
		panic("scan string failed")
	}
	return io.scanner.Bytes()
}

func (io *IO) ScanString() string {
	if !io.scanner.Scan() {
		panic("scan string failed")
	}
	return io.scanner.Text()
}

func (io *IO) ScanStrings(n int) []string {
	strs := make([]string, n)
	for i := 0; i < n; i++ {
		strs[i] = io.ScanString()
	}
	return strs
}

func (io *IO) Scan2DStrings(y, x int) [][]string {
	strings := make([][]string, y)
	for i := 0; i < y; i++ {
		strings[i] = io.ScanStrings(x)
	}
	return strings
}

func (io *IO) Scan2DGraph(y int) [][]string {
	strs := make([][]string, y)
	for i := 0; i < y; i++ {
		strs[i] = strings.Split(io.ScanString(), "")
	}
	return strs
}

func (io *IO) ScanInt() int {
	return int(io.ScanInt64())
}

func (io *IO) ScanInts(n int) []int {
	ints := make([]int, n)
	for i := 0; i < n; i++ {
		ints[i] = io.ScanInt()
	}
	return ints
}

func (io *IO) Scan2DInts(y, x int) [][]int {
	ints := make([][]int, y)
	for i := 0; i < y; i++ {
		ints[i] = io.ScanInts(x)
	}
	return ints
}

func (io *IO) ScanInt64() int64 {
	i, err := strconv.ParseInt(io.ScanString(), 10, 64)
	if err != nil {
		panic(err)
	}
	return i
}

func (io *IO) ScanFloat64() float64 {
	i, _ := strconv.ParseFloat(io.ScanString(), 64)
	return i
}

func (io *IO) ScanFloat64s(n int) []float64 {
	floats := make([]float64, n)
	for i := 0; i < n; i++ {
		floats[i] = io.ScanFloat64()
	}
	return floats
}

func (io *IO) Println(a ...interface{}) {
	fmt.Fprintln(io.writer, a...)
}