Speed up video (not only linear) so specific point is at specific time

Hey everyone,

I have a video and now I have certain time codes in the footage which have to be at a certain time in in the timeline.

These points are represented by different coloured lines in the footage and where they should be at in the timeline.

Of course I could cut the video and just adjust the speed of them seperatly but this would leed to the first speed curves.

But I want to speed up the footage to that point like shown below.

Is there a way to achieve this in premiere or is this It easier to achieve in After Effects? And if so how can I do it over there?

I'm thankful for every help

~Paul