## Powers of Two

### Problem 686

$2^7=128$ 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 $p(123, 678910)$.