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>

int Search(int,int);
int *arrayS,*arrayT;

int N,M;

int main(){
  int count=0,S;
  int i;
  scanf("%d",&N);
  arrayS = (int *)malloc(sizeof(int) * N);
  for(i=0;i<N;i++){
    scanf("%d",&arrayS[i]);
  }
  scanf("%d",&M);
  arrayT = (int *)malloc(sizeof(int) * M);
  for(i=0;i<M;i++){
    scanf("%d",&arrayT[i]);
    S=Search(0,arrayT[i]);
    if(S==1){
      printf("yes\n");
    }
  else printf("no\n");
  }
  free(arrayS);
  free(arrayT);
  return 0;
}

int Search(int i,int key){
  int res;
if(key == 0) return 1;
if(i >= N) return 0;
res = Search(i+1,key) || Search(i+1,key-arrayS[i]);
return res;
}