How to implement authentication in an android application with a firebase backend using VK?

Question

Android

Hello. I am writing an application on andoid + firebase in which there should be user authentication using mail and password, facebook and vkontakte. For the first two, it is built into the firewall, but it’s not clear with VK, everything is somehow indistinct in Google, I didn’t find anything specific. Please tell me how to do it or where to read.
And I would like one user to be able to log into his account in different ways. Let's say through VK and Facebook, if there is only one mail. What in this case should be with the mail and password? let's say at first the user registered through mail and password, and then if he wants to log in using VK, where the mail is the same, how to do it to get to this user's profile. and if at first the user logged in through VK, and then wants to register an e-mail and password with the same mail, then he should get to the profile he accessed using the social network or should the registration fail? It seems to me that it should be zayfeilitsya or provide additional ways of verification. Or generally distinguish between the entrance through social networks (if there is one mail, then they enter on one account) and mail and password, and one excludes the other, that is, if the mail was used in one case, then the second fails with this mail. In general, how do experienced progers solve these issues and / or where can I read about it?