Prelude

Consider two functions $f(x)=2^x+x-131$ , $g(x)=4^x+x+130$ . Define $h(k)$ as the number of real solution(s) of $f^{-1}(x)-g^{-1}(x)=k$ where $F^{-1}(x)$ denotes the inverse function of $F(x)$ . Denote $s$ as the sum of all $k$ values such that the function $h(k)$ has discontinuity.

Find the value of $s$ .

HINT : This problem can be solved very easily.