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: Wrong Answer)

package main

import (
	"fmt"
	"math"
)

func main() {
	var (
		n int
		x int
		y int
	)
	fmt.Scan(&n,&x,&y)

	count := make(map[int]int, n)

	for i := 0; i < n-1; i++ {
		count[i] = 0
		fmt.Println(count)
	}

	for i := 1; i < n+1; i++ {
		for j := i + 1; j < n+1; j++ {
			d1 := x - i
			d2 := y - j
			shortd := math.Abs(float64(d1)) + math.Abs(float64(d2)) + 1
			d := j - i
			if (d > int(shortd)) {
				count[int(shortd)-1] += 1
			} else {
				count[d-1] += 1
			}
		}
		fmt.Println(count)
	}
	
	for _, c := range count {
		fmt.Println(c)
	}
}