Can you figure it out? good riddle?

ok. so i went to this famous cannibal island of liars and truthtellers. i visited there because i heard of a new third group of natives settling on the insland not long ago. Vegetarians all, they loved to baffle visiting logicians by telling truth or falsehood at will. they were genially known as fakers. as i walked down a jungle pathm i noticed a crossroads up ahead where three islanders were standing. they introduced themselves and curly, larry, and moe. realizing the two of the three would enjoy having me for dinner, literally, i quickly asked the way to the village of the vegetarian fakers. with a resounding "that way" curly pointed east, larry pointed north, and moe pointed west. i guess i should have known better. trying a better tack, i asked, "which one of you is the truthteller?" curly answered, "I am the truthteller, larry is the faker, and moe is the liar". larry said, "I am the truthteller, curly is the liar, and moe is the faker". moe said, "I am the truthteller, larry is the liar, and curly is the faker”. What a fix. Exasperated, I shouted, “you cant all be telling the truth, can you?” Curly and larry quickly said “no” while moe said “yes”. This gave me the key I needed, and I reasoned thus: the liar had to answer yes; only moe answered yes; so moe was the liar. Curly had said that moe was the liar while larry had said that curly was the liar so Curly was telling the truth. I headed east. Five minutes later, I was running back, pursued by a bloodthirsty mob shouting, “you will not make a fine dinner,” “our barbecue pit is not heating up right now,” and most ominously, “you are escaping.” However, my daily jogging stood me in good stead, and I made it back to the ship. I didn’t have a chance to ask curly, larry, and moe where I had gone wrong. Con you figure it out?