KöMaL 2017 B4892

Two players, First and Second, play the following game: they place 2017 pebbles on the table. First starts by removing 1 pebble. Then Second may choose to remove either 1 or 2. Then First may remove 1, 2, 3 or 4. Then Second may remove any number from 1 to 8. And so on, the player in the $i$th step needs to remove at least 1 and at most $2^{i-1}$ pebbles. The player removing the last pebble from the table wins the game. Who has a winning strategy?