$2^7=128$ is the first power of two whose leading digits are "12".
The next power of two whose leading digits are "12" is $2^{80}$.

Define $p(L,n)$ to be the $n$th-smallest value of $j$ such that the base 10 representation of $2^j$ begins with the digits of $L$.
So $p(12,1)=7$ and $p(12,2)=80$.

You are also given that $p(123,45)=12710$.

Find $p(123,678910)$.