Rotational mechanics

A uniform rod of length $L$ and mass $2m$ rests on a smooth horizontal table. A mass $m$ moving horizontally at right angles to the rod with initial velocity $V$ collides with one end of rod and sticks to it. Determine the angular velocity of the system after collision.

If the solution can be represented as $\dfrac{aV}{bL}$ , where $a$ and $b$ are coprime positive integers, find $a+b$ .