Putnam 2017 B6

Find the number of ordered $64$-tuples $(x_0,x_1,\dots,x_{63})$ such that $x_0,x_1,\dots,x_{63}$ are distinct elements of $\{1,2,\dots,2017\}$ and $$x_0 + x_1 + 2x_2 + 3x_3 + \cdots + 63 x_{63}$$ is divisible by 2017.