Junior Mathematical Olympiad, September 2019

We say that a number is a child of another number if we can get it by placing between any two digits of the other number either nothing, a $+$, or a $\times$. For example, $145$ and $5$ are children of $12121$ because $145=12\times 12+1$ and $5=1+2\times 1+2\times 1$. The number $15$ is both a child of $12121$ and of $33333$, because $12+1+2\times 1=15=3+3+3+3+3$. Which of the following numbers is also a child of both $12121$ and $33333$? A) $18$ B) $34$ C) $39$ D) $42$ E) $45$