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 Kotlin (judge verdict: Accepted)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val a = readLine()!!.split(' ').map { it.toInt() }
    val q = readLine()!!.toInt()

    val choice = BooleanArray(n) { false }
    fun chk(m: Int) :Boolean {
        var sum = 0
        for (i in 0 until n) {
            sum += if (choice[i]) a[i] else 0
        }
        return sum == m
    }
    fun select (m: Int, d: Int): Boolean {
        arrayOf(true, false).forEach {
            choice[d] = it
            if (d+1 == n) {
                if(chk(m)) return true
            } else {
                if(select(m,d+1)) return true
            }
        }
        return false
    }

    val m = readLine()!!.split(' ')
    repeat(q) {
        val M = m[it].toInt()
        if (select(M, 0) ) println("yes")
        else println("no")
    }

}