For an arbitrary grid, Robot defines its beauty to be the sum of elements in the grid.

Robot gives you an array $a$ of length $n$ and an array $b$ of length $m$. You construct a $n$ by $m$ grid $M$ such that $M_{i,j}=a_i\cdot b_j$ for all $1 \leq i \leq n$ and $1 \leq j \leq m$.

Then, Robot gives you $q$ queries, each consisting of a single integer $x$. For each query, determine whether or not it is possible to perform the following operation exactly once so that $M$ has a beauty of $x$:

1. Choose integers $r$ and $c$ such that $1 \leq r \leq n$ and $1 \leq c \leq m$
2. Set $M_{i,j}$ to be $0$ for all ordered pairs $(i,j)$ such that $i=r$, $j=c$, or both.

Note that queries are not persistent, meaning that you do not actually set any elements to $0$ in the process — you are only required to output if it is possible to find $r$ and $c$ such that if the above operation is performed, the beauty of the grid will be $x$. Also, note that you must perform the operation for each query, even if the beauty of the original grid is already $x$.

Input

The first line contains three integers $n$, $m$, and $q$ ($1 \leq n,m \leq 2\cdot 10^5, 1 \leq q \leq 5\cdot 10^4$) — the length of $a$, the length of $b$, and the number of queries respectively.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \leq |a_i| \leq n$).

The third line contains $m$ integers $b_1, b_2, \ldots, b_m$ ($0 \leq |b_i| \leq m$).

The following $q$ lines each contain a single integer $x$ ($1 \leq |x| \leq 2\cdot 10^5$), the beauty of the grid you wish to achieve by setting all elements in a row and a column to $0$.

Output

For each testcase, output "YES" (without quotes) if there is a way to perform the aforementioned operation such that the beauty is $x$, and "NO" (without quotes) otherwise.

You can output "YES" and "NO" in any case (for example, strings "yES", "yes" and "Yes" will be recognized as a positive response).

见题面 Input 部分

见题面 Output 部分

In the second example, the grid is

0 -2 5 0 -3

0 4 -10 0 6

0 -6 15 0 -9

0 0 0 0 0

0 0 0 0 0

By performing the operation with $r=4$ and $c=2$, we create the following grid:

0 0 5 0 -3

0 0 -10 0 6

0 0 15 0 -9

0 0 0 0 0

0 0 0 0 0

which has beauty $4$. Thus, we output YES.

In the second query, selecting $r=3$ and $c=5$ creates a grid with beauty $-3$.

In the third query, selecting $r=3$ and $c=3$ creates a grid with beauty $5$.