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-----
5 2 4

-----Sample Output-----
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.

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