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KöMaL 2026 C1910

    Bogi likes to play with pebbles which she calls gems. Currently she has 4052 gems, and she labeled them with numbers 1, 2, 3, ..., 4052. She wants to place her gems in a red and a blue box such that for every k=1k=1, 2, 3, ..., 2026 gems with label kk and 2k2k should be in different boxes. How many ways can Bogi distribute her gems?

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