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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Globalization;
using System.Linq;
using System.Net.Sockets;

namespace ALDS1_5_A
{
    class Program
    {
        static void Main(string[] args)
        {
            n = int.Parse(Console.ReadLine());
            A = ReadInt();
            int q = int.Parse(Console.ReadLine());
            int[] m = ReadInt();

            dp = new int[n + 1, 2001];
            for (int i = 0; i <= n; i++)
            {
                for (int j = 0; j <= 2000; j++)
                {
                    dp[i, j] = -1;
                }
            }

            for (int i = 0; i < q; i++)
            {
                bool ans = Solve(0, m[i]);
                if (ans) Console.WriteLine("yes");
                else Console.WriteLine("no");
            }

            Console.ReadKey();
        }

        static int[,] dp;
        static int n;
        static int[] A;
        static bool Solve(int i, int m)
        {
            if (m == 0) return true;
            else if (m < 0) return false;
            if (i >= n) return false;
            if (dp[i, m] != -1) return dp[i, m] == 1 ? true : false;

            bool ret = Solve(i + 1, m) || Solve(i + 1, m - A[i]);
            
            if (ret) dp[i, m] = 1;
            else dp[i, m] = 0;
            return ret;
        }


        static int[] ReadInt()
        {
            int[] ret = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return ret;
        }
        static long[] ReadLong()
        {
            long[] ret = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return ret;
        }
    }
}