Problem Statement

Ms. AtCoder has decided to distribute chocolates to N friends on Valentine's Day. For the $i-th friend (1 \leq i \leq N),$ she wants to give a square chocolate bar of size $2^{A_i} \times 2^{A_i}$.
She has procured a rectangular chocolate bar of size $H \times W$. It is partitioned by lines into a grid of H rows and W columns, each cell being $a 1 \times 1$ square.
Determine whether it is possible to divide the chocolate bar along the lines into several pieces to obtain all the chocolate bars for her friends. It is fine to have leftover pieces.

Input

The input is given from Standard Input in the following format:
H W N
$A_1 A_2 \cdots A_N$

Output

If the objective is achievable, print Yes; otherwise, print No.

Constraints

• $1 \leq H \leq 10^9$
• $1 \leq W \leq 10^9$
• $1 \leq N \leq 1000$
• $0 \leq A_i \leq 25$ \ $(1 \leq i \leq N)$
• All input values are integers.

Sample Input 1

4 4 4
1 0 0 1

Sample Output 1

Yes

By dividing $a 4 \times 4$ chocolate bar as shown in the figure below, you can obtain pieces of size $2 \times 2, 1 \times 1, 1 \times 1, 2 \times 2$.

Sample Input 2

5 7 6
0 1 0 2 0 1

Sample Output 2

Yes

By dividing $a 5 \times 7$ chocolate bar as shown in the figure below, you can obtain pieces of size $1 \times 1, 2 \times 2, 1 \times 1, 4 \times 4, 1 \times 1, 2 \times 2$.

Sample Input 3

3 2 7
0 0 0 0 0 0 0

Sample Output 3

No

It is impossible to obtain seven pieces of size $1 \times 1$ from $a 3 \times 2$ chocolate bar.

Sample Input 4

11 11 2
2 3

Sample Output 4

No

It is impossible to obtain both $a 4 \times 4$ and an $8 \times 8$ piece from an $11 \times 11$ chocolate bar.

Sample Input 5

777 777 6
8 6 9 1 2 0

Sample Output 5

Yes

见题面 Input 部分

见题面 Output 部分