I'll be living on a small atoll in the Cook Islands for a month and I can pack food in my suitcase. Would love some advice on eating frugally on a remote island!

Basically, the island is surrounded by fish and, according to a friend who's been there, you don't fish, you catch, so there'll be an abundance of seafood. There's adequate cooking facilities so I'm thinking of bringing dry pasta/lentils/rice, tortillas, oils, seasoning/spices, oinions, garlic, lemons, limes and a couple of bags of nuts and some confectionary for snacking purposes. This being said, I feel like I can add a bit more variety. I'm going with a family who'll bring cryo-vacuumed steaks amongst other things but I'd appreciate some advice on what else I can/should bring with me so I don't have to spend a fortune on food over there!