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>
#define N 2000

int C[N];

extern int search(int n,int C[],int i,int h){
  if(h==0){
    return 1;
  }
  else if(i>=n){
    return 0;
  }

  return (search(n, C, i + 1 ,h) || search(n, C, i + 1, h - C[i]));
}

extern void solve(int n,int C[],int q,int H[]){
  int i;
  for(i=0;i<q;i++){
    if(search(n,C,0,H[i])==1)
      printf("yes\n");
    else
      printf("no\n");
  }
}

int main(){
  int n,*H,q,i;
  scanf("%d",&n);

  for(i=0;i<n;i++){
    scanf("%d",&C[i]);
  }
  scanf("%d",&q);
  H=(int*)malloc(sizeof(q));
  for(i=0;i<q;i++){
    scanf("%d",&H[i]);
  }
  
  solve(n,C,q,H);
  
  return 0;
}