The positive integral solutions of the equation $x^y=y^x$ are $(2,4)$, $(4,2)$ and $(k,k)$ for all $k>0$.

For a given positive integer $n$, let $f(n)$ be the number of integral values $0<x,y\le n^2-n$ such that $$x^y\equiv y^x(\mathrm{mod}n).$$ For example, $f(5)=104$ and $f(97)=1614336$.

Let $S(M,N)=\sum f(p)$ where the sum is taken over all primes $p$ satisfying $M\le p\le N$.

You are given $S(1,{10}^2)=7381000$ and $S(1,{10}^5)\equiv 701331986(\mathrm{mod}993353399)$.

Find $S({10}^{16},{10}^{16}+{10}^6)$. Give your answer modulo $993353399$.