CSES Traffic Lights Question

Problems and Contests
#1

Link to Question: CSES - Traffic Lights.
I’m confused regarding what the question is asking.

If we’re looking at the input:
8 3
3 6 2
I’m confused about why the output is:
5 3 3
Shouldn’t the output be:
5 3 2

Regarding the last one, there the next upcoming light is on the 3rd position, while the previous light is on the 0th position. Thus the output should be 2 right?

These 2 users had the same question, but I don’t understand their explanation:

Thanks!

#2

It’s the largest section of the whole road without traffic lights. The gap between 3…6 is still 3, even after adding a light at position 2.

#3

after adding the lights, wouldn’t the result would be:

1 2 3 4 5 6 7 8
  x x     x

with the longest segment being from [4,5] or [7,8] which is length 2

edit: oops i misread the question (even after i solved it 2 months ago)
the traffic lights are considered as points while we’re supposed to calculate the maximum “distance” between two existing traffic lights.