Frame

Interview

Time limit5sMemory limit256 MB

Summary

You must answer YES or NO for each of N bar lengths based on whether bars of that length tile the one-cell-thick X by Y frame.

Level: Medium5 of 10
Topics: Math, Brute force
Solved: No attempts yet

Problem

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.

Input

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 $A_K$ ( $1 \le A_K \le 10^6$ ).

Output

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.

Examples5

Example 1
Input
```
5 6
2
3
4
```
Expected output
```
YES
NO
```
Example 2
Input
```
3 3
5
1
2
3
4
8
```
Expected output
```
YES
YES
NO
NO
NO
```

Example 3

Input

Expected output

YES
YES
YES
NO
NO
NO

Example 4
Input
```
3 5
6
2
3
4
5
6
12
```
Expected output
```
YES
YES
NO
NO
NO
NO
```
Example 5
Input
```
5 5
4
4
5
8
16
```
Expected output
```
YES
NO
NO
NO
```