Consider $f(x) = 1 + 5x + 6x^2 + 3x^3 + 10x^4 + 11x^5 - 19x^6 - 2x^7$

Consider $g(x) = x^5-1$

Let $R(k,x)$ be the remainder obtained when $f(x)^k$ is divided by $g(x)$.

Example :

$$R(1,x) = 12-14x+4x^2+3x^3+10x^4$$

$$R(2,x) = -112-247x+352x^2+60x^3+172x^4$$

Let $S(k,x)$ be the sum of coefficient of $R(k,x)$.

You need to enter the value of $S(18^{10^{18}},x)$ modulo $100086841$.