Frame

Take an $X \times Y$ rectangle of unit cells and cut out the middle $(X - 2) \times (Y - 2)$ rectangle. The figure that remains is a frame of size $X \times Y$. A frame is a border one cell thick, so it has $2X + 2Y - 4$ cells.

You have an unlimited supply of $A \times 1$ tiles. A tile can be rotated by 90 degrees. Tiles must stay inside the frame and must not overlap. Decide whether the frame can be paved completely with these tiles. For example, a frame of size $5 \times 6$ can be paved with $3 \times 1$ tiles, but it cannot be paved with $4 \times 1$ tiles.

The first line contains two integers $X$ and $Y$ ($3 \le X \le 10^6$, $3 \le Y \le 10^6$).

The second line contains an integer $N$, the number of tile types to analyze ($1 \le N \le 1000$).

Each of the next $N$ lines contains one integer. The integer on the $K$-th of those lines is $A_K$ ($1 \le A_K \le 10^6$).

Print $N$ lines. The $K$-th line contains YES if a frame of size $X \times Y$ can be paved with $A_K \times 1$ tiles, and NO if it cannot.