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"
	"container/list"
	"fmt"
	"os"
	"strconv"
)

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

	ans := make([]int, n+1)
	for i := 1; i <= n; i++ {
		seen := make([]int, n+1)
		seen[i] = 1
		ls := list.New()
		ls.PushBack(i)
		for ls.Len() > 0 {
			v := ls.Remove(ls.Front()).(int)
			if nv := v - 1; nv >= 1 && nv <= n && seen[nv] == 0 {
				seen[nv] = seen[v] + 1
				ans[seen[nv]-1]++
				ls.PushBack(nv)
			}
			if nv := v + 1; nv >= 1 && nv <= n && seen[nv] == 0 {
				seen[nv] = seen[v] + 1
				ans[seen[nv]-1]++
				ls.PushBack(nv)
			}
			if v == x && seen[y] == 0 {
				seen[y] = seen[x] + 1
				ans[seen[y]-1]++
				ls.PushBack(y)
			}
			if v == y && seen[x] == 0 {
				seen[x] = seen[y] + 1
				ans[seen[x]-1]++
				ls.PushBack(x)
			}
		}
	}

	var wr = bufio.NewWriter(os.Stdout)
	for i := 1; i < n; i++ {
		wr.WriteString(strconv.Itoa(ans[i]/2) + "\n")
	}
	wr.Flush()
}