Passing game (problem solution)

example

topic

Ideas

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This question seems to be very simple. Think of people with restrictions as dots, and other consecutive segments as a dot (in fact, unlimited people). At the same time, $1$ is also regarded as a point. (The standard practice is to treat all free people as a single point, which I think is complicated).

Then every mmEnumerate all$m$ rounds, judge the limit alone, and then the time complexity is:$O\left(mk\right)$ , but my practice has an extra 2 constant, QAQ, I didn't dare to write code.

And why is this question DP? ? ?

Shouldn't it be called thinking? ? ?