2016 is coming!

Algebra Level 4

$x_{1}^{2016} + x_{2} ^{2016} +\cdots+ x_{2016}^{2016}$

If $x_{1}, x_{2},\ldots, x_{2016}$ are the roots of the equation $x^{2016} - 2016x - 2 = 0,$ then find the value of the expression above.