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 input contains several test cases, each of them as described below.

The first line contains 2 integers - **X** and **Y**.

The second line contains integer **N** - the number of tile types to be analyzed.

Each of the following **N** lines contains one integer, not exceeding 10^{6}. We designate with **A _{k}** the integer on the

**(k+2)**line of the input.

^{th}# Output

For each test case, your goal is to print **N** lines, where the K^{th} line should contain the word 'YES', if it is possible to tile the **X×Y** sized frame with tiles **A _{k}×1**, and the word 'NO' otherwise.

# Constraints

- 3 <= X, Y <= 10
^{6} - 1 <= N <= 1000

# Sample

Input | Output |
---|---|

5 6 2 3 4 | YES NO |