Zhar, ancient one attack

By Rasiel, in Arkham Horror Second Edition

Hi,

I have a question about this ancient one. We dont agree how his attack works so, is it

a) first round he give zhar token to the first player, second round he kills first player

b) first round he gives zhar token to first player, second round gives zhar token to second player, until all players have zhar token, then kills one investigator who is first player

we ask because it says only that he gives zhar token to the first player only if no player has a zhar token... says nothing about what happens if a player do ...

thanks for your reply ...

From what I read in BGG, mode A sounds like the better way.