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)

N, X, Y = map(int, input().split())
ans = {}
for i in range(N):
    # print(i+1)
    # print()
    for j in range(i+1, N):
        diff = (j+1)-(i+1)
        if i+1 <= X and j+1 >= Y:
            diff = diff - (Y-X)+1

        elif X+1 == i+1 and j+1 == Y and X+1 != j+1:
            # print("Yes")
            diff -= 1
        elif j+1 == Y-1 and X >= i+1 and X+1 != j+1:
        # print("Yes")
            diff -= 1

        if diff == 0:
            diff += 1
        # print(i+1, j+1, diff)



        tmp = ans.get(diff)

        if tmp == None:
            ans[diff] = 1
        else:
            ans[diff] = tmp + 1

# print(ans)
for i in range(N-1):
    tmp = ans.get(i+1)
    if tmp == None:
        tmp = 0
    print(tmp)