H. Hiring Candidates Game
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

There has been a selection process in your company. According to the evaluation criteria, there is a tie between $$$n$$$ candidates. For the final selection phase, your Human Resources coordinator has designed a game to possibly filter some of them since they want to reduce the personnel cost.

The game goes as follows:

  1. The $$$n$$$ candidates form a circle, all of them are looking to its center. Then, some candidate is assigned with the id $$$1$$$, the one to its left is assigned with the number $$$2$$$ and so on.
  2. Then, two supervisors $$$s_{1}$$$ and $$$s_{2}$$$ stand behind of the candidates with ids $$$1$$$ and $$$n$$$, respectively.
  3. If the number of candidates left is at most $$$2$$$, then finish the game and hire those candidates.
  4. Otherwise, the supervisor $$$s_{1}$$$ moves counting $$$r$$$ candidates (including its own position) in clockwise direction and then stops and the supervisor $$$s_{2}$$$ moves counting $$$c$$$ candidates (including its own position) in counter-clockwise direction and then stops. Then, there are two possibilities:
    1. Both $$$s_{1}$$$ and $$$s_{2}$$$ reached the same candidate. In this case, remove the candidate from the circle and hire him/her.
    2. $$$s_{1}$$$ and $$$s_{2}$$$ reached different candidates. In this case, remove both and don't hire any of them.
  5. Return to Step 3.

Given the scenario of the game, compute the candidates that will be hired according to the game.

Input

The first line of input contains three integers $$$n$$$, $$$r$$$ and $$$c$$$ ($$$1 \leq n \leq 10^{4}$$$ and $$$1 \leq r, c \leq 10^{5}$$$) — The number of candidates, the number of candidates that $$$s_{1}$$$ counts while moving and the number of candidates that $$$s_{2}$$$ counts while moving, respectively.

Output

Print a single line — The sequence of ids of the hired candidates in ascending order.

Examples
Input
5 3 3
Output
2 3 4
Input
4 4 3
Output
1 3
Input
6 5 2
Output
1 2 5 6
Note

The following is the process of the game until it stops for the first sample case:

The candidate with id $$$3$$$ is hired after the first iteration, then the candidates with ids $$$1$$$ and $$$5$$$ are removed and rejected after the second iteration and only the candidates with ids $$$2$$$ and $$$4$$$ are left. Since there are only $$$2$$$ candidates, the game stops and both of them are hired. In the end, the candidates with ids $$$2$$$, $$$3$$$ and $$$4$$$ are hired.