Problem:
Exhaustive Search

Write a program which reads a sequence A of n elements and an integer M, and outputs "yes" if you can make M by adding elements in A, otherwise "no". You can use an element only once.

You are given the sequence A and q questions where each question contains Mi.

Input

In the first line n is given. In the second line, n integers are given. In the third line q is given. Then, in the fourth line, q integers (Mi) are given.

Output

For each question Mi, print yes or no.

Constraints

n ≤ 20

q ≤ 200

1 ≤ elements in A ≤ 2000

1 ≤ Mi ≤ 2000

Sample Input 1

5
1 5 7 10 21
8
2 4 17 8 22 21 100 35

Sample Output 1

no
no
yes
yes
yes
yes
no
no

Notes

You can solve this problem by a Burte Force approach. Suppose solve(p, t) is a function which checkes whether you can make t by selecting elements after p-th element (inclusive). Then you can recursively call the following functions:

solve(0, M)

solve(1, M-{sum created from elements before 1st element})

solve(2, M-{sum created from elements before 2nd element})

...

The recursive function has two choices: you selected p-th element and not. So, you can check solve(p+1, t-A[p]) and solve(p+1, t) in solve(p, t) to check the all combinations.

For example, the following figure shows that 8 can be made by A[0] + A[2].

Solution in Scala (judge verdict: Runtime Error)

import scala.io.StdIn.{readInt, readLine}
object Main {
    def main(args: Array[String]): Unit = {
        val len = readInt
        val list = readLine.split(" ").map(_.toInt).toList
        readInt
        readLine.split(" ").map(_.toInt).foreach { target =>
            if (search(list, len, target)) println("yes") else println("no")
        }
    }
    def search(haystack: List[Int], len: Int, target: Int): Boolean = {
        if (len == 0) {
            false
        } else if (combinationExists(haystack, Nil, target, len)) {
            true
        } else {
            search(haystack, len - 1, target)
        }
    }
    // haystack から count 個の要素を足し合わせて target になる組み合わせがあるかどうかを調べる。
    def combinationExists(haystack: List[Int], elems: List[Int], target: Int, count: Int): Boolean = {
        if (count == 0) {
            if (elems.sum == target) true else false
        } else {
            haystack match {
                case Nil => false
                case x :: xs if (elems.sum > target) => false
                case x :: xs => {
                    if (combinationExists(xs, x :: elems, target, count - 1)) {
                        true
                    } else {
                        combinationExists(xs, elems, target, count)
                    }
                }
            }
        }
    }
}