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)

#include <stdio.h>
#include <stdlib.h>

int check(int n, int m, int *A, int M, long sum) {
  if(m == n) {
    if (sum == M) {
      return 1;
    }
    return 0;
  }
  int v0 = check(n,m+1,A,M,sum);
  if (v0 == 1) {
    return 1;
  }
  if (sum + A[m] <= M) {
    int v1 = check(n,m+1,A,M,sum+A[m]);
    if (v1 == 1) {
      return 1;
    }    
  }

  return 0;
}

  

int main()
{
  int i,n,*A,q,M;
  scanf("%d",&n);
  A = (int*)malloc(sizeof(int) * n);
  for (i = 0; i < n; i++) {
    scanf("%d",A+i);
  }
  scanf("%d",&q);
  for (i = 0; i < q; i++) {
    scanf("%d",&M);
    if(check(n,0,A,M,0) == 1) {
      printf("yes\n");
    }else {
      printf("no\n");
    }
  }
  
  
  return 0;
}