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 collections import deque
N, X, Y = map(int, input().split())

adj = [[] for i in range(N)]
for i in range(N):
    if i != 0 and i != N-1:
        adj[i].append(i-1)
        adj[i].append(i+1)
    elif i == 0:
        adj[i].append(1)
    else:
        adj[i].append(N-2)
    if i == X-1:
        adj[i].append(Y-1)
    if i == Y-1:
        adj[i].append(X-1)

dists = []
for i in range(N):
    dist = [-1]*N
    q = deque([i])
    dist[i] = 0
    while q:
        l = q.popleft()
        d = dist[l]
        for w in adj[l]:
            if dist[w] > -1:
                continue
            dist[w] = d + 1
            q.append(w)
    dists.append(dist)
ans = [0 for i in range(N-1)]
for i in range(N):
    for k in range(1, N):
        ans[k-1] += dists[i].count(k)
for i in range(N-1):
    ans[i] = ans[i]//2
print(*ans, sep='\n')