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)

def main():
    n, x, y = map(int, input().split())
    # n, x, y = 7, 3, 7
    edge = [[] for _ in range(n+1)]
    dist = [[abs(i-j) for i in range(n+1)] for j in range(n+1)]
    counter = [0 for i in range(n)]
    for i in range(1, n):
        edge[i].append(i+1)
        edge[i+1].append(i)
    edge[x].append(y)
    edge[y].append(x)
    # print(edge)
    for i in range(x):
        for j in range(y, n+1):
            dist[i][j] = j-y + x-i +1
            dist[j][i] = j-y + x-i +1
    for i in range(x, x+(y-x)//2):
        for j in range(y, n+1):
            dist[i][j] = j-y + i-x + 1
            dist[j][i] = j-y + i-x + 1
    for i in range(x):
        for j in range(y-(y-x)//2+1, y):
            dist[i][j] = y-j + x-i + 1
            dist[j][i] = y-j + x-i + 1
    for i in range(x, x+(y-x)//4):
        for j in range(y-(y-x)//4, y):
            dist[i][j] = y-j + i-x + 1
            dist[j][i] = y-j + i-x + 1

    for i in range(1, n+1):
        for num in dist[i][1:]:
            counter[num] += 1
    # print(dist)

    for num in counter[1:]:
        print(num//2)
    
if __name__=='__main__':
    # import time
    # start = time.time()
    main()
    # print(f"{time.time()-start}[s]")