Taxi#8367
Alina wants to order a taxi using a popular app. Several drivers are ready to accept her request.
Alina is a responsible person and wants to pick the most experienced driver, i.e., the driver who has completed the most rides. However, the app does not show the number of trips each driver has completed. The only information available to Alina is each driver's rating.
After each ride, a passenger rates the driver with an integer from to inclusive. The driver's rating is calculated as the arithmetic mean of all received ratings.
Write a program to determine the minimum number of trips a driver must have completed to achieve a rating equal to exactly (without rounding).
The input contains a single real number (1 \leq R \leq 5), representing the driver's rating with a precision of up to decimal places.
Print a single natural number on the first line: the minimum number of trips. If it is impossible to obtain the specified rating, print -1.
If the rating is achievable, print on the second line non-negative integers --- the number of ratings 1, 2, 3, 4, 5 the driver received, respectively. If there are multiple possible distributions of ratings that achieve the minimum, you may print any of them.
Пример 1
Subtask | Points | Additional Constraints | Required Subtasks |
|---|---|---|---|
0 | 0 | Sample tests | - |
1 | 41 | The precision of is at most decimal place | - |
2 | 33 | The precision of is at most decimal places | 0, 1 |
3 | 26 | The precision of is at most decimal places | 0, 1, 2 |