Python Account Checker Tool

I need a Python-based program to verify a large list of accounts on https://firstmail.ltd/en-US/webmail/login. You will receive a .txt file containing thousands or even millions of accounts in the format Email:Password. The program should:

- Log in attempts to check account validity
- Save working accounts to a separate .txt file
- Handle high volume efficiently

Ideal Skills and Experience:
- Proficiency in Python
- Experience with web automation and login scripts
- Familiarity with handling large data sets
- Knowledge of error handling and performance optimization

Please ensure the solution is robust and can manage potentially high loads without crashing.