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 Ruby (2.3.3) (judge verdict: Accepted)

def min(x, y)
	x < y ? x : y
end

def shortest_distance(i, j, n, x, y)
	if i <= x && y <= j
		(x - i) + (j - y) + 1
	elsif i <= x && j < y
		dist = min(y - j + 1, j - x)
		(x - i) + dist
	elsif x < i && y <= j
		dist = min(i - x + 1, y - i)
		(j - y) + dist
	elsif x < i && j < y
		min(j - i, i - x + y - j + 1)
	end
end

def function(n, x, y)
	counts = Array.new(n, 0)
	(1...n).each do |i|
		((i + 1)..n).each do |j|
			distance = shortest_distance(i, j, n, x, y)
			counts[distance] += 1
		end
	end
	(1...n).each do |k|
		puts counts[k]
	end
end

n, x, y = gets.chomp.split.map(&:to_i)
function(n, x, y)