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 JAVA (judge verdict: Memory Limit Exceeded)


import java.io.IOException;
import java.io.InputStream;
import java.util.HashMap;
import java.util.NoSuchElementException;

public class Main  {
    static int[] a;
    // static int[] qu;
    static HashMap hp = new HashMap<Integer, Boolean>();

    public static void main(String[] args) {
        StringBuilder sb = new StringBuilder();
        FS fs = new FS();
        int n = fs.nextInt();
        a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = fs.nextInt();
        }
        int q = fs.nextInt();
        //    qu = new int[q];
        boolean j=true;
        for (int i = 0; i < q; i++) {
            int t = fs.nextInt();
            // if (hp.containsKey(t)) {
            //     if( hp.get(t).equals(true)){
            //         sb.append("yes\n");
            //         continue;
            //     } else {
            //         sb.append("no\n");
            //         continue;
            //     }
            // }
            if (solve(0,t)) {
                sb.append("yes\n");
              //  hp.put(t, true);
            } else {
            //    hp.put(t, false);
                sb.append("no\n");
            }

        }
        System.out.print(sb.toString());
    }

    private static boolean solve(int p, int t) {
        if (hp.containsKey(t)) {
           if(!(Boolean) hp.get(t))return false;
        }
        if (t == 0) {

            return true;
        }
        if (t < 0 || p >= a.length) {
            return false;
        }
        return solve(p + 1, t - a[p]) || solve(p + 1, t);
    }

    static class FS {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            return hasNextByte() ? buffer[ptr++] : -1;
        }

        private boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        private void skipUnprintable() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
        }

        public boolean hasNext() {
            skipUnprintable();
            return hasNextByte();
        }

        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public int nextInt() {
            return (int) nextLong();
        }

        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }
    }
}