https://stackoverflow.com/questions/69534589/counting-the-number-of-ways-to-make-up-a-string/6953654

============
2 substrings

          Original:   p   p   k   p   k   e
Decompositions (4):  (p   p   k)         (e)
                     (p   p)         (k   e)
                     (p)         (p   k   e)
                         (p)     (p   k   e)

============
3 substrings

          Original:   p   p   k   p   k   e
Decompositions (8):  (p   p) (k)         (e)
                     (p) (p   k)         (e)
                     (p   p)         (k) (e)
                     (p) (p)         (k   e)
                     (p)         (p   k) (e)
                     (p)         (p) (k   e)
                         (p)     (p   k) (e)
                         (p)     (p) (k   e)

============
4 substrings

          Original:   p   p   k   p   k   e
Decompositions (4):  (p) (p) (k)         (e)
                     (p) (p)         (k) (e)
                     (p)         (p) (k) (e)
                         (p)     (p) (k) (e)