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.

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.

Constraints

• $3 \leq N \leq 2 \times 10^3$
• $1 \leq X,Y \leq N$
• X+1 < Y
• All values in input are integers.

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

见题面 Input 部分

见题面 Output 部分