Dreamr the Pool Guy

Revision en5, by dreamr, 2019-02-11 05:03:34

Hi there!

I recently thought up a very interesting problem, so I will introduce it to you guys.


One day, when I (Dreamr) was in the pool teaching a swimming lesson held in the neighborhood pool center, I was thinking about the inefficiency of the process for the upcoming exam. There are n (1 <= n <= 100,000) pools in the swimming center and m(1 <= m <= 100,000) students who would participate in the exam.


Dreamr, the owner of the center, already knew about the duration (every di <= 10^9) of each student that will take the exam. Only one student at a time can be in one pool and the test can be run simultaneously in multiple pools. Dreamr is a really lazy person, so he hopes to make the minimum of the maximum time of each pool's total used time. However, Dreamr is not a super bright person. Thus, Dreamr only wants to know a solution that is close to the actual answer: Your output can be smaller than or equal to 2 times the correct optimal solution. (Extra challenge: In the comments try to prove why the problem would be impossible to solve if you have to get the actual optimal solution/answer.)

Please help Dreamr solve this challenging problem.

Input

2 5

3 3 5 7 8

Output

13

3 3 7

5 8

Note

In the first test case, there are 2 pools and 5 people. If Dreamr assigns 3, 3, 5 to the first pool and 7, 8 to the second pool, then it takes 11 and 15 minutes, respectively, so the maximum time is 15. If Dreamr assigns 3, 3, 7 to the first pool and 5, 8 to the second pool, then it takes both 13 minutes, so the maximum time is 13.

13 < 15 so the optimal solution would be 13.

Thus, your output can be smaller than or equal to 26 in this case.


Sorry for my bad English <3

Thanks for reading and happy problem-solving!

-dreamr

Tags challenging_problems, hard problem

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en5 English dreamr 2019-02-11 05:03:34 122
en4 English dreamr 2019-02-11 05:02:01 1 Tiny change: 'ay, when I(Dreamr) w' -> 'ay, when I (Dreamr) w'
en3 English dreamr 2019-02-11 05:01:44 62
en2 English dreamr 2019-02-11 04:05:29 312 (published)
en1 English dreamr 2019-02-11 03:58:56 1747 Initial revision (saved to drafts)