Angle Combination Problem

Given N initial angles a_i and M target angles b_i, determine for each target angle b_i whether it can be obtained by adding and subtracting any number of the initial angles. Note that each initial angle a_i can be used any number of times (including zero) in the operations.

Mathematically, you need to decide if for each b_i there exists integers x₁, x₂, …, x_N (which can be negative, zero, or positive) such that:

[ b_i = x_1 \times a_1 + x_2 \times a_2 + \cdots + x_N \times a_N ]

A key observation is that the set of values that can be obtained using integer combinations of a_i is exactly the set of all multiples of (d), where (d) is the (\gcd(a_1, a_2, \ldots, a_N)). Therefore, the answer for a given b_i is "YES" if and only if (d) divides (b_i); otherwise, it is "NO".

inputFormat

The first line contains an integer N denoting the number of initial angles. The second line contains N space-separated integers representing a₁, a₂, ..., a_N. The third line contains an integer M denoting the number of target angles. The fourth line contains M space-separated integers representing b₁, b₂, ..., b_M.

outputFormat

Output M lines. The i-th line should be "YES" if the target angle b_i can be obtained by adding and subtracting any number of the initial angles; otherwise, output "NO".

sample

3
1 2 3
4
1 5 7 4

YES
YES
YES
YES