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 PyPy3 (2.4.0) (judge verdict: Accepted)

#N, X, Y = map(int, input().split())
#l = [0 for _ in range(N-1)]
#for i in range(1, N+1):
#    for j in range(i+1,N+1):
#        n = min(j-i, abs(i-X)+1 + abs(j-Y))
#        l[n-1] +=1
#for m in l:
#    print(m)
inf = 100000
N, X, Y = map(int, input().split())
X -= 1
Y -= 1
ans = [0] *N
for i in range(N):
    queue = []
    dist = [inf] *N
    def push(n, d):
        if dist[n] == inf:
            dist[n] = d
            queue.append(n)
    push(i, 0)
    for q in queue:
        if q-1 >=0:
            push(q-1, dist[q] + 1)
        if q+1 <N:
            push(q+1, dist[q] + 1)
        if q == X:
            push(Y, dist[q] + 1)
        if q == Y:
            push(X, dist[q] + 1)
    for d in dist:
        ans[d] += 1
for i in range(1, N):
    print(int(ans[i]/2))