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: Time Limit Exceeded)

from sys import stdin
from queue import Queue


def main():
    n, x, y = [int(x) for x in stdin.readline().rstrip().split()]
    x -= 1
    y -= 1
    ans = [0] * n
    for i in range(n):
        dist = [None] * n
        q = Queue()

        def push(d, v):
            if v < 0 or n <= v:
                return
            if dist[v] is not None:
                return
            dist[v] = d
            q.put(v)

        push(0, i)
        while not q.empty():
            v = q.get()
            d = dist[v]
            push(d + 1, v - 1)
            push(d + 1, v + 1)
            if v == x:
                push(d + 1, y)
            if v == y:
                push(d + 1, x)

        for d in dist:
            ans[d] += 1

    ans = [x // 2 for x in ans]
    print(*ans[1:], sep='\n')


if __name__ == "__main__":
    main()