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)

import queue
n,x,y = map(int,input().split())
ans = {}
for i in range(1,n):
    dist = [-1]*n
    q = queue.Queue()
    dist[i-1] = 0
    q.put(i)
    while True:
        if q.empty():
            break
        else:
            a = q.get()
            if a > 1 and dist[a-2] == -1:
                dist[a-2] = dist[a-1]+1
                q.put(a-1)
            if a < n and dist[a] == -1:
                dist[a] = dist[a-1]+1
                q.put(a+1)
            if a == x and dist[y-1] == -1:
                dist[y-1] = dist[a-1]+1
                q.put(y)
            if a == y and dist[x-1] == -1:
                dist[x-1] = dist[a-1]+1
                q.put(x)
    for j in range(i,n):
        s = dist[j]
        if s in ans.keys():
            ans[s] += 1
        else:
            ans[s] = 1
for k in range(1,n):
    if k in ans.keys():
      print(ans[k])
    else:
      print(0)