You are given an array a containing N positive integers. You have to create a new array b from the given array.

The elements of the array b can be evaluated by using the equation $b_j$ = $\sum_{i=1}^{j} a_i * 2^{j-i}$.

There are Q queries to be answered. In each query, a single integer $p_i$ is given and asked if it is possible to get $p_i$ by adding some of the elements of the array b. If it is possible, print Yes else print No.

Input format

• The first line of input contains a single integer N.
• Next line contains N space-separated integers $a_i$.
• Next line contains a single integer Q.
• The last line of input contains Q space-separated integers $p_i$.

Output format

Print Q space-separated strings, where $i_{th}$ string is an answer to the $i_{th}$query.

Constraints

• $1 \le n,a_i \le 10^5$
• $1 \le q \le 10^3$
• $1 \le p_i \le 10^{10}$