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 Python (3.4.3) (judge verdict: Wrong Answer)

def min_distance(a,b,x,y):
  if a <= x and y <= b:
    # ショートカットをはさむ場合
    return (b-a - (y-x)+1)
  else:
    if x <= a and y <= b:
      # 左端がショートカットの中の場合
      s1 = b - a
      s2 = (a-x) + 1 + (b-y)
      if s1 < s2:
        # 順周り
        return s1
      else:
        # 戻って
        return s2
    elif a <= x and b <= y:
    # ショートカットの中の場合
      s1 = (b-a)
      s2 = (x-a) + 1 + (y-b)
      if s1 < s2:
        return s1
      else:
        return s2
    else:
      return (b-a)
nxy = input('').split(' ')
n = int(nxy[0])
x = int(nxy[1])
y = int(nxy[2])

for k in range(1,n):
  cnt = 0
  for i in range(1,n+1):
    for j in range(i+1,n+1):
      s = min_distance(i,j,x,y)
      if s == k:
        cnt+=1
  print(cnt)