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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
)

var sc *bufio.Scanner

const bufferSize = 1024

func nextInt() int {
	if !sc.Scan() {
		panic(nil)
	}
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

var production bool

func debugf(format string, v ...interface{}) {
	if !production {
		fmt.Printf(format, v...)
	}
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

func min(a ...int) int {
	res := a[0]
	for i := 1; i < len(a); i++ {
		if res > a[i] {
			res = a[i]
		}
	}
	return res
}

func answer(reader io.Reader, writer io.Writer) {
	sc = bufio.NewScanner(reader)
	buf := make([]byte, bufferSize)
	sc.Buffer(buf, 1e+7)
	sc.Split(bufio.ScanWords)
	n := nextInt()
	x := nextInt() - 1
	y := nextInt() - 1
	ans := make([]int, n-1)
	debugf("n: %d, x: %d, y: %d\n", n, x, y)

	for i := 0; i < n-1; i++ {
		for j := i + 1; j < n; j++ {
			d := min(j-i, abs(x-i)+abs(y-j)+1, abs(x-j)+abs(y-i)+1)
			ans[d-1]++
		}
	}

	for i := range ans {
		_, _ = fmt.Fprintf(writer, "%d", ans[i])
		if i != len(ans)-1 {
			_, _ = fmt.Fprint(writer, "\n")
		}
	}
}

func main() {
	production = true
	answer(os.Stdin, os.Stdout)
}