Question

Shortest Distance Between Vertex

We have an undirected graph G with N vertices and N edges. The vertices are numbered from 1 to N.

For all i = 1, 2, 3,. , N-1, there is an edge between vertex i and vertex i+1.

There is one other edge between vertex A and vertex B.

Now for each k from 1 to N-1, solve the following problem:

Find the number of pairs (i, j) such that the shortest distance between vertex i and vertex j is k.

For all i = 1, 2, 3,. , N-1, there is an edge between vertex i and vertex i+1.

There is one other edge between vertex A and vertex B.

Now for each k from 1 to N-1, solve the following problem:

Find the number of pairs (i, j) such that the shortest distance between vertex i and vertex j is k.

Input

The only line of the input contains three integers N, A and B.

Constraints:

3 <= N <=2 × 10

1 <= A, B <= N

A+1 < B

Constraints:

3 <= N <=2 × 10

^{3}1 <= A, B <= N

A+1 < B

Output

For each k = 1, 2,. , N-1, print the answer for the following case in a new line.

Example

Sample Input 1:

5 2 4

Sample Output 1:

5

4

1

0

Sample Input 2:

3 1 3

Sample Output 2:

3

0

Sample Input 3:

10 4 8

Sample Output 3:

10

12

10

8

4

1

0

0

0

5 2 4

Sample Output 1:

5

4

1

0

Sample Input 2:

3 1 3

Sample Output 2:

3

0

Sample Input 3:

10 4 8

Sample Output 3:

10

12

10

8

4

1

0

0

0