Problem - https://cses.fi/problemset/task/1163

I am not getting this problem.I think the sample output is incorrect!

Input:

8 3

3 6 2

Output:

`5 3 3`

According to sample input answer should be : 5 3 2 but sample output is 5 3 3

Demonstration:

```
0 1 2 3 4 5 6 7 8
! ! !
```

I mean after adding 2 how the longest path without traffic light is 3 and not 2?

Somebody please help.Is there a catch which i am losing?