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 20
#define Q 200
#define true 1
#define false 0

int solve(int, int);
int n, A[N];

int main(){
  int q, m, a, i;

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

  scanf("%d", &q);
  if(q > Q) exit(3);
  for(i=0; i<q; i++){
    scanf("%d", &m);
    if(m < 1 || m > 2000) exit(4);
    a = solve(0,m);
    if(a == 1) printf("yes\n");
    else if(a == 0)printf("no\n");
    else printf("%d\n",a);
  }
  return 0;
}

int solve(int i, int m){
  int res;
  
  if(m == 0) return true;
  if(i >= n) return false;
  res = solve(i+1,m) || solve(i+1,m-A[i]);
  return res;
}