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>

void print(int *,int *,int,int);
int Calc(int,int,int,int *);

int main()
{
  int n1,*A,n2,*Q,i;
  
  scanf("%d",&n1);

  A = (int *)malloc(n1 * sizeof(int));

  for(i=0;i<n1;i++){
    scanf("%d",&A[i]);
  }

  scanf("%d",&n2);

  Q = (int *)malloc(n2 * sizeof(int));

  for(i=0;i<n2;i++){
    scanf("%d",&Q[i]);
  }

  print(A,Q,n2,n1);
  
  free(A);
  free(Q);

  return 0;
}

void print(int *A,int *Q,int n2,int n1)
{
  int i;
  
  for(i=0;i<n2;i++){
    if(Calc(0,Q[i],n1,A)==0) printf("no\n");
    else printf("yes\n");
  }
}

  
int Calc(int i,int Q,int n1,int *A)
{
  int res;
  
  if(Q==0) return 1;
  if(i>=n1) return 0;

  res = Calc(i+1,Q,n1,A)+Calc(i+1,Q-A[i],n1,A);

  return res;
}