# Crazy function

Algebra Level 5

$\begin{cases} f(1) = 0 \\ f(2)=1 \\ f(4)=2 \\ f(8)=3 \\ f(16)=4 \\ f(32)=5 \end{cases}$

Let $$f(x)$$ be a polynomial of degree 5 satisfying the system of equations above. If the coefficient of $$x$$ in $$f(x)$$ can be expressed as $$\dfrac pq$$, where $$p$$ and $$q$$ are coprime positive integers, find $$p+q$$.

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