Frame

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

Figure 1. A frame of size 5 × 6

Figure 2. A frame of size 5 × 6, paved with tiles of size 3 × 1

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

Input Specification

The first input line contains two integers X and Y (3 ≤ X ≤ 10⁶, 3 ≤ Y ≤ 10⁶). The second line contains an integer N, the number of tile types to be analyzed (1 ≤ N ≤ 1000). Each of the following N lines contains one integer, not exceeding 10⁶. Let's denote the integer on the (K + 2)-th line of the input with A_K.

Output Specification

Output N lines, where the Kth line should contain the word “YES“ if it is possible to tile the frame of size X × Y with tiles of size A_K × 1, and the word “NO“ otherwise.

Sample Input

1. 5 6
2. 2
3. 3
4. 4

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Output for Sample Input

1. YES
2. NO

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Original Problem

Southeastern Europe Regional Contest, 2014