SMO 2016 Open Round 1 Question 16

Let $f(x)=x^{2016}+a_{2015}x^{2015}+a_{2014}x^{2014}+\cdots+a_1 x+a_0$ be a polynomial such that f(i)=2 i -1 for all i=1,2,...,2015. Find the value of $f(0)+f(2016)-2016!$.