Does the emission of semen due to lustful thoughts and slight, unintentional physical movement invalidate the fast, and what should a fasting person do in this case?

If semen is emitted merely by thinking without masturbating, the fast is valid according to the majority of scholars. However, if semen is emitted due to masturbation, the fast is invalidated, and repentance and making up the fast are obligatory, but expiation is not required.