Bored of waiting for his plane to travel to the International Mathematics Olympiad, Daniel began to write powers of $2$ in a list in his notebook as follows: $\bullet$ Starting with the number $1$, Daniel writes the next power of $2$ at the end of his list and reverses the order of the numbers in the list. Let us call such a modification of the list, including the first step, a move. The list in each of the first $4$ moves it looks like this: $$1 \,\,\,\, \to 2, 1 \,\,\,\, \,\,\,\, \to 4, 1, 2 \,\,\,\, \,\,\,\, \to 8, 2, 1, 4$$Daniel plans to carry out operations until his plane arrives, but he is worried let the list grow too. After $2020$ moves, what is the sum of the first $1010$ numbers?