are you sure becuase it works when i test your case

I am seeing your comment every where , whould You explain why it would fail?

As many others, the solution fails for n=625, p=2 (the case from the text). Also, C-style cast...

As many others, the solution fails for n=625, p=2 (the case from the text).

Again, the solution like this fails for an example from the text n=695, p=2.
The error comes from static_cast of double power to int.
See an example:

cout << std::pow(5,4) << ' ' << static_cast(std::pow(5,4)) << '\n';

This one fails for an example from the text n=695, p=2