Anybody? :(

cnt(s, p) = k for some p. Notice that
0 + 1 + ... + (k-1) = (k^2 — k) / 2 = "that sum" for some p.
You can find "that sum" for all p by using data structure described in editorial.

So to find sum(k^2) you need to multiply it by 2 and add sum(k), which is a number of substrings of s.