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: Time Limit Exceeded)

N, X, Y = gets.chomp.split(" ").map(&:to_i)

# A = Array.new(N) {|a| a = Array.new(N)}
A = Array.new(N*N)
# A = {}
# 1.upto(N-1){|i| A[i] = {}}

1.upto(N-1) do |k|
  ans = 0
  1.upto(N-1) do |i|
    c0 = i + k
    if c0 <= N
      if A[i * N + c0].nil?
        A[i * N + c0] = k
        ans += 1
      end
      if (i <= X && i + k > X) || (i > X && i - X < k)
        s = k - ((X - i).abs + 1)
        [Y+s, Y-s].uniq.select{|v| v <= N && v != i && (v - i).abs > k }.each do |c|
          a, b = [i, c]
          a, b = [b, a] if a > b
          if A[a * N + b].nil?
            A[a * N + b] = k
            ans += 1
          end
        end
      end
    end
  end
  puts ans
end