Liam has a coin that lands heads with probability $\frac{2}{7}$, and Noah has a coin that lands on heads with probability $\frac{3}{8}$. Liam and Noah alternately toss their coins until someone gets a head; the first one to get a head wins. All coin tosses are independent. Liam goes first. The probability that Liam wins is $\frac{p}{q}$ where $p$ and $q$ are relatively prime positive integers. What is $q-p$?