Maximum deflection angle!

Classical Mechanics Level 4

A mass $M$ collides elastically with a stationary mass $m$ . If $(M < m)$ , then it is possible for $M$ to bounce directly backwards. However, if $(M > m)$ , then there is a maximum angle of deflection of $M$ . Find the correct relation between $\theta , m, M$ .

( $\theta$ is the maximum angle of deflection.)

Question Source - Maximum deflection angle