CF830A Office Keys

There are $ n $ people and $ k $ keys on a straight line. Every person wants to get to the office which is located on the line as well. To do that, he needs to reach some point with a key, take the key and then go to the office. Once a key is taken by somebody, it couldn't be taken by anybody else. You are to determine the minimum time needed for all $ n $ people to get to the office with keys. Assume that people move a unit distance per $ 1 $ second. If two people reach a key at the same time, only one of them can take the key. A person can pass through a point with a key without taking it.

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In the first example the person located at point $ 20 $ should take the key located at point $ 40 $ and go with it to the office located at point $ 50 $ . He spends $ 30 $ seconds. The person located at point $ 100 $ can take the key located at point $ 80 $ and go to the office with it. He spends $ 50 $ seconds. Thus, after $ 50 $ seconds everybody is in office with keys.