Define a function f(n)=n+⌊n⌋.
Find the smallest value of k such that the composite function,
fk(2017)=k timesf∘f∘f∘⋯∘f(2017) can be expressed as m2 for some positive integer m.
Submit your answer as m−k.
Notation: ⌊⋅⌋ denotes the floor function.
This problem is inspired from a Putnam problem.