Prophet’s Hut

Hello. Please help me understand how to debug a quest in the prophet's hut. I read the manual, and it helped, but not completely. The map is for multiplayer. The quest is to kill specific neutral creatures (by script name) for a reward. The problem is that after a monster dies (even if one player takes the reward), when other players visit the prophet's hut, they are still given the quest, and the next time, it is marked as failed. How can I make it so that the quest is not given to other players after the monster is dead (the quest condition has been met), and the reward is given only to the player who fulfilled this condition?