Help with picture to go on Mug

I need help trying to get a picture on a mug.
Basically it needs to have that warped form to look good once it’s rolled around a mug.
This is what I mean:
And the attached pcture is what I’m trying to get on.
Any help would be appreciated.

I think its fine the way it is. Mugs are flat so there really isnt a reason to curve it. If it was a bottle then it might need to be curved.

Oh, we just figured it needed to be curved because of the image maker on the website I linked.