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>

#define TRUE 1
#define FALSE 0

int solve(int,int);

int n,a[2000],j=0;

int main(){
  int m[2000],q,re,i;

  scanf("%d",&n);
  for(i = 0;i < n;i++){
    scanf("%d",&a[i]);
  }
  scanf("%d",&q);
  for(i = 0;i < q;i++){
    scanf("%d",&m[i]);
  }

  for(i = 0;i < q;i++){

    re = solve(j,m[i]);

    if(re == TRUE){
      printf("yes\n");
    }
    else{
      printf("no\n");
    }
  }

  return 0;

}

int solve(int j,int m){

  if(m == 0){
    return TRUE;
  }
  if(j >= n){
    return FALSE;
  }

  if(solve(j+1,m) == TRUE || solve(j+1,m-a[j]) == TRUE){
    return TRUE;
  }
  j = j + 1;

}