(Mishnah): All seven days, [the Kohen Gadol] throws the blood [of the Temidim], burns the Ketores, fixes the Neros, and offer the head and legs [and all the limbs - PNEI MOSHE];

All other days, if the Kohen Gadol wanted to offer, he is first (chooses what he wants) to offer, and first to take a portion (picks what he wants).

(Gemara) Question: (How can he offer? All seven days they sprinkle Mei Chatas on him.) Is he not Tamei due to his Haza'ah?!

Answer (R. Yosi bei R. Bun): After he offered the Korbanos, they sprinkled on him [and he immersed afterwards].