A lantern with a mass of M hanging from the end of a massless chain of length L is shown below. The chain is fixed to a pivot point at the top, allowing the lantern to swing freely. A bird with a mass of m flies directly towards the lantern at a velocity $\vec{v}$ and crashes into it, becoming embedded. Determine the magnitude of minimum velocity $\vec{v}$ that the bird must have to ensure the lantern, now with the bird inside, swings completely over the top of its arc.

• A. $\sqrt{g L}\left(1+\frac{M}{m}\right)$
• B. $\sqrt{2 g L}\left(1+\frac{M}{m}\right)$
• C. $\sqrt{5gL}(1+\frac{M}{m})$
• D. $4 \sqrt{g L}\left(1+\frac{M}{m}\right)$