Middle European Mathematical Olympiad 2013 Problem T-8

The expression $$\pm \square \pm \square \pm \square \pm \square \pm \square \pm \square$$ is written on the blackboard. Two players, $A$ and $B$, play a game, taking turns. Player $A$ takes the first turn. In each turn, the player on turn replaces a symbol $\square$ by a positive integer. After all the symbols $\square$ are replaced, player $A$ replaces each of the signs $\pm$ by either $+$ or $-$, independently of each other. Player $A$ wins if the value of the expression on the blackboard is not divisible by any of the numbers $11, 12, \ldots, 18$. Otherwise, player $B$ wins.

Determine which player has a winning strategy.