Frame

Time Limit: 10 Seconds    Memory Limit: 131072 KB

Let's consider a  X×Y  rectangle with  the  middle  (X  –  2)×(Y  –  2)  rectangle  cut out. We will call this figure a frame with size X×Y. Picture 1 shows the frame 5 × 6.


Let's  assume  that  we  have  unlimited  number  of  tiles  with  size  A×1.  We  consider  the  following problem:  is it possible to completely  pave  a  frame with size  X×Y  using  these tiles  (tiles can be rotated by 90 degrees). For example, frame 5×6 from Picture 1 can be paved completely with tiles of size 3×1 (one way to do so is shown in Picture 2), but can’t be paved with tiles of size 4×1.

Input

The first  input  line contains 2 integers  –  X  and  Y  (3 ≤  X  ≤ 106 ,  3 ≤  Y  ≤ 106). The second line  contains integer N  –  the number of tile  types  to be analyzed (1 ≤ N ≤ 1000). Each of following  N lines contains one integer,  not  exceeding  106. We  designate  with  AK  the integer  on the  (k+2)-th  line of the input file.

Output

Your goal is to print  N  lines,  where the  K-th line should contain the word "YES", if it is possible to tile the frame with size X × Y with tiles AK × 1, and the word "NO" otherwise.

Sample Input

5 6
2
3
4

Sample Output

YES
NO
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