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"

var (
	N int
	X int
	Y int
)

func main() {
	fmt.Scan(&N, &X, &Y)

	m := make(map[int]int)
	for i := 1; i <= N-1; i++ {
		for j := i + 1; j <= N; j++ {
			m[d(i, j)]++
		}
	}
	for k := 1; k < N; k++ {
		fmt.Println(m[k])
	}
}

func min(x1, x2, x3, x4 int) int {
	var x12, x34 int
	if x1 < x2 {
		x12 = x1
	} else {
		x12 = x2
	}
	if x3 < x4 {
		x34 = x3
	} else {
		x34 = x4
	}
	if x12 < x34 {
		return x12
	}
	return x34
}

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

func d(i, j int) int {

	// 1. i -> j
	// 2. i -> X -> j
	// 3. i -> Y -> j
	// 4. i -> X -> Y -> j

	d1 := abs(j - i)
	d2 := abs(j-X) + abs(X-i)
	d3 := abs(j-Y) + abs(Y-i)
	d4 := abs(X-i) + 1 + abs(Y-j)

	return min(d1, d2, d3, d4)
}