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I'd say call the 3-bet and bet-fold the turn. It seems a lot of the time a K would smooth call the flop and raise the turn, so his flop 3-bet makes me suspicious.

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That doesnt make sense imo. If you believe he doesnt have the K you should just call down and maybe raise the river. Why make him fold a worse hand which he would bluff at you. If I were to do anything different and I dont put him on a K I would cap flop and bet fold turn and river.