Berlian Championship#3534
In the capital city of New-Prog in Berlandia, a programming championship is about to take place. of the top participants have gathered in the city. The organizers, unprepared for such a large turnout, are faced with a challenge: how to provide server access to each participant?
To connect to the server, each participant must activate their IP address, which is represented as an integer between and 10^9. However, due to an oversight, some participants may have the same IP address. To activate an IP address, a special Berlandian device called a seport (server port) is used.
A seport operates with a specific range . Once activated at a frequency , it can activate frequencies within the range [T-R, T+R]. The organizers have only identical seports available. Your task is to determine the minimum range for the seports and the minimum number of seports required so that all participants can activate their IP addresses.
The first line contains two integers and , where 1 \leq N, K \leq 10^5. The second line contains integers x_i, representing the IP address of the -th participant, with 1 \leq x_i \leq 10^9 and 1 \leq i \leq N.
Output two numbers: the minimum number of seports needed and the minimum range of their operation, with a precision of decimal places.
Example 1