Fat Cantor Set question

hj2000

Let C be the thick Cantor set. let {a_n} be a sequence of positive numbers.
In the construction of the thick Cantor set, at the n-th stage we remove the middle a_n part of each interval (instead of the middle third as in the ordinary Cantor set).

I actually wanted to show that [0,1]-C is dense (where C is the thick Cantor set). How do I show it?