Reflection principle for the modulus of the Brownian Motion

Question

I have the following question. Suppose we define $M(t)=\sup_{0\le s\le t}|B(s)|$, where $B$ is an ordinary Brownian motion in $\mathbb{R}$. How can we compute $P(M(t)\ge a)$? Is it $2P(|B(t)|\ge a)$? I tried immitating the Moerters proof, but having two reflection points makes it more difficult...