$A$ and $B$ are blocks of same mass $m$ exactly equivalent to each other. Both are placed on a frictionless surface connected by a spring. The natural length of the spring is $L$ and the force constant is $K$. Initially,the spring is at its natural length. Another equivalent block $C$ of mass $m$ travelling at speed $v$ along the line joining $A$ and $B$ collides with $A$. In an ideal condition,the maximum compression of the spring is:

• A
  $v \sqrt{\frac{m}{2K}}$
• B
  $m \sqrt{\frac{v}{2K}}$
• C
  $\sqrt{\frac{mv}{K}}$
• D
  $\frac{mv}{2K}$