How much multiplying will you do?

Calculus Level 3

\[ \large \displaystyle \int_{0}^{1} x^{2016} (1-x)^{2017} \, dx \]

If the above integral can be expressed in the form \( \dfrac{a}{b} \), where \( a\) and \( b \) are coprime positive integers, find \( a \).

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