ffmpeg fast accurate cut

Question

I want to cut a part of Video file without re-encoding whole video. This is the method came to my mind:

first.mp4:

ffmpeg -i in.mp4 -ss start_cut -t start_to_a first.mp4

last.mp4:

ffmpeg -i in.mp4 -ss b -t b_to_end last.mp4

middle.mp4

ffmpeg -i in.mp4 -ss a -t a_to_b -c copy middle.mp4

then merge these three files with:

merge -f concat -i fileslist -c copy out.mp4

I tested this method but it's not giving expected output the 3 video files are cut ok but after merging the middle part slows down and has low quality in out.mp4.

What is the problem with this method? Or is there another method to fast accurate cut?

Thank you.