What major should a graduate student study if he wants to be a lawyer or a prosecutor?

No problem. Whether undergraduate or graduate, in fact, the focus of study should be to have a good opportunity to lay a good theoretical foundation and learn to judge legal relations. If you choose to be a lawyer or a prosecutor in the future, the key is actually future practice. Personally, I think that as a student, it is unrealistic to determine the so-called development direction at present. The final choice direction may only be decided by your region, your guiding lawyer or prosecutor, your hobbies, etc. You will go to work again in the future, and these choices are probably not directly related to your professional choice.