dreamr's blog

By dreamr, history, 12 days ago, In English,

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

 
 
 
 
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12 days ago, # |
Rev. 2   Vote: I like it +5 Vote: I do not like it

how do u solve this? this is such a good problem! LOVE IT!!!!

Nice job!

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12 days ago, # |
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Auto comment: topic has been updated by dreamr (previous revision, new revision, compare).

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11 days ago, # |
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Does anyone have a solution?

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11 days ago, # |
Rev. 4   Vote: I like it +1 Vote: I do not like it
Solution