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.