Two identical blocks $$A$$ and $$B$$ each of mass $$m$$ resting on the smooth horizontal floor are connected by a light spring of natural length $$L$$ and spring constant $$K$$. A third block $$C$$ of mass $$m$$ moving with a speed $$v$$ along the line joining $$A$$ and $$B$$ collides with $$A$$. The maximum compression in the spring is:

A

$$v\sqrt{\frac{m}{2K}}$$

B

$$\sqrt{\frac{mv}{2K}}$$

C

$$\sqrt{\frac{mv}{K}}$$

D

$$\sqrt{\frac{m}{2K}}$$