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<string.h>
#include <stdlib.h>
int searchfront(int,int*,int,int,int);
int search(int,int*,int,int,int);
int main(){
  int i,j,n,nr[20],q,qr[200];
  scanf("%d",&n);
  for(i=0;i<n;i++)
    scanf("%d",&nr[i]);
  scanf("%d",&q);
  for(i=0;i<q;i++)
    scanf("%d",&qr[i]);
  for(i=0;i<q;i++){
    if(searchfront(n,nr,0,0,qr[i]) == 1) printf("yes\n");
    else printf("no\n");
  }
    
}
int searchfront(int n,int *a,int m,int all,int key){
  int i,ans;
  for(i=0;i<n;i++){
    ans =  search(n,a,i,all,key);
    if(ans == 1) return 1;
  }
  return 0;

}

int search(int n,int *a,int m,int all,int key){
  int i,ans;
  all += a[m];
  // if(key ==17)  printf("%d %d \n",all,m);
  if(key == all) return 1;
  if(all > key) return 0;
  for(i=m+1;i<n;i++){
    ans = search(n,a,i,all,key);
    if(ans == 1) return 1;
  }
  return 0;

}