Find the number that gives the max number of steps for the Euclidean Algorithm

Question

I assume that $a$, $b$ are integers $a > b > 0$.

$N(a,b)$ denotes the number of steps taken in the Euclidean Algorithm to find $\gcd(a,b)$, for example, $N(7,2) = 2$. $M(a)$ then denotes the maximal $N(a,b)$, for example, $M(7) = 3$.

How can I then find the $b$ for any given a such that $N(a,b)$ is maximal?