To which one of the following schools of philosophy did Kumarila Bhatt

To which one of the following schools of philosophy did Kumarila Bhatta and Prabhakara belong?

Lokayata
Madhyamika
Purva-Mimamsa
Uttara-Mimamsa
This question was previously asked in
UPSC CDS-2 – 2022
Kumarila Bhatta and Prabhakara were two prominent philosophers of the Purva-Mimamsa school of Indian philosophy. They developed differing interpretations within the Mimamsa tradition.
Purva-Mimamsa is one of the six orthodox (astika) schools of Hindu philosophy, primarily concerned with the interpretation of the Vedas, particularly the ritualistic sections (Karma Kanda).
Lokayata is a heterodox (nastika) materialistic school. Madhyamika is a school of Mahayana Buddhism founded by Nagarjuna. Uttara-Mimamsa is another name for the Vedanta school, which focuses on the philosophical sections of the Vedas (Jnana Kanda), particularly the Upanishads.