Mistakenly used DEP's Apple ID to login to iCloud.com

Now whenever I try login to idmsa.apple.com, it will go thru the password login authentication page, but it goes in to a loop of asking to send a verification code.

It will send a verification code, but when I enter the code, it will just go back to asking me to hit Continue to send a verification code.

I knew that I should not use the DEP ID for iCloud or iTunes based on the Apple Deployment Programs Help:

Important: Don’t use this new Apple ID with an iTunes or iCloud account, or any other Apple services or website other than the Apple ID for Students program and the Volume Purchase Program. Doing so causes the Apple ID to stop working with all Apple Deployment Programs.

But accidents happens, especially when you use multiple Apple IDs for different services on a computer. 😊

Anybody had the same issue in the past? Any help to resolve this would be greatly appreciated.