Frame paving#8376
Frame x \times y is rectangle x \times y with center rectangle (x - 2) \times (y - 2) dropped out. We have many tiles a \times 1. Is it possible to pave frame x \times y with tiles a \times 1? Tiles can be rotated 90 degrees.
For example, frame 5 \times 6 can be tiled with tiles 3 \times 1, but not with tiles 4 \times 1.
The first line contains two positive integers and ( ≤ , ≤ 10^6). The second line contains one positive integer ( ≤ ≤ ) - number of tile types. The third line contains positive integers not greater than 10^6 - lengths of tiles.
Print lines with or . -th line contains if it is possible to tile the frame with tiles of -th type. Output otherwise.
Exemple 1