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)

# coding:utf-8
n, x, y = map(int, input().split())
for k in range(1, n):
    if k == 1:
        print(n)
    # elif y - x > k:
    #     if (n - y) + (x - 1) + 1 < k:
    #         print(n)
    #     else:
    #         ans = 0
    #         right = n - y
    #         left = x - 1
    #         if right + left + 1 >= k:
    #             for i in range(min(right, left)):
    #                 if k - i - 1 <= max(right, left):
    #                     ans += 1
    #         print(ans)
    else:
        ans = 0
        for i in range(1, n - k + 1):
            if i + k < y:
                ans += 1
            elif x < i:
                ans += 1
        right = n - y
        left = x - 1
        if right + left + 1 >= k:
            for i in range(min(right, left) + 1):
                if k - i - 1 <= max(right, left):
                    ans += 1
        print(ans)