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<stdlib.h>

#define TRUE 1
#define FALSE 0

int solve(int, int);
int n;

int A[200];

int main(){
  int q, i, j;
  int m[2000];
  
  scanf("%d",&n);
  if( n>20 ) exit(1);

  for( i=0 ; i<n ; i++ ){
    scanf("%d",&A[i]);
    if( A[i]<1 || 2000<A[i] ) exit(2);
  }

  scanf("%d",&q);
  if( q>200 ) exit(3);

  for( i=0 ; i<q ; i++ ){
    scanf("%d",&m[i]);
    if( m[i]<1 || 2000<m[i] ) exit(4);
  }

  for( i=0 ; i<q ; i++ ){
    if(solve(0,m[i]) == TRUE ) printf("yes\n");
    else printf("no\n");
  }
  
  return 0;
}

int solve(int i, int m){
  int res1, res2;
  
  if( m==0 ) return TRUE;
  if( i>=n ) return FALSE;

  res1 = solve(i+1, m);
  res2 = solve(i+1, m-A[i]);

  if( res1 == TRUE || res2 == TRUE ) return TRUE;
  else return FALSE;
}