Which is larger?

Which is larger

$1008 ^ { 2017} \quad \text{ or } \quad 1009 ^ { 1009 } \times 1007 ^ {1008} ?$

Hint: $a_n = \left( 1 + \dfrac{1}{n} \right)^{n+1}$ for $n = 1, 2, 3, \ldots$ is a decreasing sequence.