Four friends, Alice, Bob, Charlie and Dave, meet one Sunday afternoon to play a game of cards. There are 35 cards, each labelled with a unique positive integer between 1 and 35, inclusive. They are placed face-up on a table. In each round, each player takes turns removing one card from the table.
In the first round, a player is allowed to remove any card. From the second round onwards, a player is allowed to remove any card labelled with a number which is the difference of the numbers of two cards that have been removed before. The game ends when nobody can remove a card. The last one to remove a card from the table wins.
In each round, Alice takes the first turn, followed by Bob, Charlie and David, in that order. Alice did not remove a card with a multiple of 7 in the first round. Who can definitely win the game?