The Goldbach conjecture deals with expressing integers as sums of primes. One might also seek to express integers as sums of other numbers, such as the Fibonacci numbers, which begin 0, 1, 1, 2, 3, 5, 8, 13, 21... For example, 26 can be written as 13+8+5 or 21+3+2. Zeckendorf (and Lekkerkerker before him) showed that every positive integer can be uniquely expressed as the sum of non-consecutive Fibonacci numbers. The Zeckendorf expansion for 26 is 21+5.
Write a function to determine the Zeckendorf expansion of the input number. In particular, output in decreasing order the Fibonacci numbers to be used in the sum.
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