How do you quickly remove sheet vinyl with coving in bathroom?

by Denise
The vinyl is old and very thick and has shrunk away from corners and along shower. I want to remove the glue from the coving area and paint walls down to the floor (with new narrow baseboard instead of coving). What is the proper way to remove the glue? The floor is underlayment or plywood I believe. Do I need to remove all glue in order to install large tile squares?

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