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 solve(int,int,int,int*);
int main(){
  int i,n,q;
  int *A;
  int *m;

  scanf("%d",&n);
  if(n>20) exit(8);
  A = (int *)malloc(n*sizeof(int));
  for(i=0;i<n;i++)
    {
      scanf("%d",&A[i]);
      if(A[i]<1 || A[i]>2000) exit(8);
    }
  scanf("%d",&q);
  if(q>200) exit(8);
  m = (int *)malloc(q*sizeof(int));
  for(i=0;i<q;i++)
    {
      scanf("%d",&m[i]);
      if(m[i]<1 || m[i]>2000) exit(8);
    }
  
  for(i=0;i<q;i++)
    {
      if(solve(0,m[i],n,A) == 1)
	{
	  printf("yes\n");
	  continue;
	}
      printf("no\n");
    }
  return 0;
}
int solve(int i,int m,int n,int *A){
  int res;
  if(m==0) return 1;
  if(i>=n) return 0;
  res = solve(i+1,m,n,A);
  if(res == 1) return res;
  res = solve(i+1,m-A[i],n,A);
  if(res == 1) return res;
  return res;
}