The equation
$$ (x-1)(x-2)\cdots(x-2016) = (x-1)(x-2)\cdots(x-2016) $$
is written on the board, with $2016$ linear factors on each side. What is the least possible value of $k$ for which it is possible to erase exactly $k$ of these $4032$ linear factors so that at least one factor remains on each side and the resulting equation has no real solutions?

Let's think step by step and output the final answer within \boxed{}.
user