Teen survival story with a helpful crow

I read a book some years ago as part of a school assignment, and I want to read it again but I don't know the title and google is no help. It was about two boys stranded on an island in the middle of nowhere. I don't remember their names or how they got on the island but I remember them fighting and arguing a lot, and I remember them finding a tree on the beach with the corpse of an old pilot (I think) leaning against it. They encountered a corvid of some kind, a crow or raven, that annoyed one of the boys but the other one found it endearing. They found an old cabin in the woods and settled there, managing to fish up a lot of breeding salmon, some of which they hung up in the cabin to dry/cure in case they're still on the island come winter. At some point the bird is found pecking at the hanging fish and chased off, but the boys realise after its gone that it was trying to reach maggots in the fish, and that none of the salmon are actually safe to eat. At the end of the book a bear attacks the boys and the bird distracts it enough for them to run off, but the bear kills it. One of the boys decides to put it up in the corpse tree rather than bury it, and in the tree he finds a nest, and in the nest is a single battery, which he puts in a radio and uses to contact authorities and get them both off the island.