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 (
	"fmt"
)

func main() {
	// Code for D - Line++
	var n, x, y int
	fmt.Scanf("%d %d %d", &n, &x, &y)

	c := map[int]int{}

	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			if i == j {
				continue
			}

			r := Min([]int{
				Abs(j - i),
				Abs(x - 1 - j) + Abs(y - 1 - i) + 1,
				Abs(x - 1 - i) + Abs(y - 1 - j) + 1,
			})

			k, ok := c[r]
			if ok {
				c[r] = k + 1
			} else {
				c[r] = 1
			}
		}
	}

	for k := 1; k <= n-1; k++ {
		s, ok := c[k]
		if ok {
			fmt.Println(s / 2)
		} else {
			fmt.Println(0)
		}
	}
}

func Abs(x int) int {
	if x < 0 {
		return - x
	}

	return x
}

func Min(l []int) int {
	m := l[0]
	for _, x := range l {
		if x < m {
			m = x
		}
	}

	return m
}