I read in an interview that from the beginning(or rather from her first album on) Ayu was allowed to choose which melodys(out of a big number of melodys) to use and these melodys then were arranged. But she wasn't interested in music at all before Duty era.
The reason she started writing was because none of the melodys her staff wrote for M appealed to her, she bought a keyboard but, not being able to play it(so the story about her playing piano at the age of 5 must be fake), hummed the melody instead.
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