35136번 - Food Rating 스페셜 저지다국어

In the new food delivery app Touch, customers are able to rate the driver with integer scores from $L$ to $R$ inclusive. Drivers will get a bonus based on how high their average rating is. However, some drivers may abuse this system. A driver delivering food to $1$ customer may get $5.0$ average rating, while another driver delivering food to $5$ customers may get $4.8$ average rating.

As the owner of the app, you need to ensure fairness in the bonus system. To do that, you need to know: for a driver to have an average rating of exactly $X$, what is the minimum number of delivery $k$, such that there exists a scenario where the average rating given by $k$ customers is exactly $X$. In addition to that, output any list of $k$ integers within $L$ to $R$ such that the average of the list is exactly $X$.

The first line contains a real number $X$ ($0 \le X \le 1000$). The number $X$ contains at most $6$ digits, including both digits before and after the decimal separator (if any).

The second line contains two integers $L$ and $R$ ($1 \le L \le R \le 1000$).

If there exists a scenario where a driver can get an average rating exactly $X$, output in the first line, the minimum integer $k$ representing the minimum number of customers giving the rating. In the next line, output $k$ integers between $L$ and $R$ representing the rating given by the customers.

If there is no such scenario, output $-1$ in a single line.

Explanation of Sample 1: The average of $[10, 9, 10, 7, 7]$ is exactly $8.6$. It can be proven such that there is no valid list with four or less integers.