On a unlimited two-dimensional plane, the plane is separated into two-dimensional grid point by line $x=k$, $x=-k$, $y=k$, $y=-k$ ($k$ is integer). There is a game like this : A king could move to any one of the neighbor $8$ grid points from the current grid point; The devil could destroy any grid point except the grid point where the king is located; The king couldn't move to the grid point which has already been destroyed by the devil. The initial grid point is $(0, 0)$. The king moves firstly, then the devil moves. The question is :
a) what A should satisfy so that the devil has a strategy to win to make the king constraint under line $y=A$ .
b) what B should satisfy so that the devil could constraint the king out of the region $x\geq B$, $y\geq B$.
c) Prove that integer $C$ exists so that the devil has a strategy to win to make the king constraint in the region $-C\leq X\leq C$, $-C\leq y\leq C$.