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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
  implicit none
  integer :: N, X, Y
  integer :: i, j, distance
  integer, allocatable :: npath(:)

  read(*,*) N, X, Y
  allocate(npath(N-1))
  npath(:) = 0

  do j = 1, N-1
    do i = j+1, N
      if(i<=X)then
        distance = i - j
      elseif(j>=Y)then
        distance = i - j
      elseif(j <=X .and. Y<=i)then
        distance = i - j -(Y-X-1)
      elseif(X <=j .and. i<=Y)then
        distance = min(i-j, (j-X)+(Y-i)+1)
      elseif(j<= X .and. X < i .and. i <= Y)then
        distance = (X-j) + min(i-X, Y-i+1)
      else
        distance = (i-Y) + min(Y-j, j-X+1)
      endif
      npath(distance) = npath(distance) + 1
    enddo
  enddo

  do i = 1, N-1
    write(*,*) npath(i)
  enddo

end program main