Would a hb 31 lens hood fit a 55-200 lens?

I want a bigger lens hood for my Nikkor lens 55-200. I see that the HB 31 hood is alot bigger. Would it fit my 55-200 lens?

I'm pretty sure the 55-200mm lens has a 52mm filter thread

There are a couple of reasons not to spend $40 for the HB 31 lens hood.

One and foremost, the HB 31 is designed for the AF-S DX Zoom-Nikkor 17-55mm f/2.8G and would be almost as effective as no hood at all.
Two, the filter size of the 55-200 mm is 52 mm and the 17-55 mm is 77 mm so would not fit in any case

The correct lens hood for your 55-200 mm is the HB-37 Bayonet Lens Hood

Certain lens hood are for certain lens