Optimize for Bgil Midol's slicing scoring

Question

In Bgil Midol's question, the score of a sequence of slice is defined as

sumof|startslices|∗2+sumof|endslices|∗2+sumof|stepslices|∗3

Such scoring method makes multiple slices possibly take less score, e.g.

• [::25] 75
• [::5][::5] 30

Given the length of a string, an upper bound of number of slices¹, and the one slice it equals to², output a way of slicing with lowest score. You can assume that the result after slicing isn't empty.

6 1 [3:4]         -> [3:-2]
6 9 [3:4]         -> [:-2][-1:]
1000 1 [::25]     -> [::25]
1000 2 [::25]     -> [::5][::5]
1000 9 [1::25]    -> [1::5][::5]
1000 9 [5::25]    -> [::5][1::5]
9100 9 [90::91]   -> [::-91][::-1]

Shortest code in each language wins.

^{1. Notice that [:] is a valid slice with no effect to score}

^{2. It can be proven that every sequence of slice can equal to one slice for a fixed string before slice}