Condition to fall into $1/r^2$ potential

Suppose we have a particle of mass $m$ coming from infinity towards the neighborhood of the origin in a potential of the form $-1/r^2$.

It is clear that the behaviour of the particle depends on the impact parameters. It is also intuitive to see that for a given incoming velocity, if this impact parameter is small enough, the particle will fall towards the origin because it can't escape the attraction.

My question is, what is the maximal impact parameter below which this falling happens? And how do you derive it?