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 true 0
#define false 1

int solve(int, int);
int n;
int A[20];

int main(){
  int i;
  int q;
  int m[200];
  int sol;

  scanf("%d", &n);
  if(20 < n)
    exit(0);
  
  for(i = 0; i < n; i++){
    scanf("%d", &A[i]);
    if(A[i] < 1 || 2000 < A[i])
      exit(1);
  }

  scanf("%d", &q);
  if(200 < q)
    exit(2);
  
  for(i = 0; i < q; i++){
    scanf("%d", &m[i]);
    if(m[i] < 1 || 2000 < m[i])
      exit(3);
  }

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

  return 0;
}

int solve(int i, int m){
  int res;

  if(m == 0)
    return true;
  if(n <= i)
    return false;

  res = solve(i+1, m);
  if(res == true)
    return res;
  res = solve(i+1, m-A[i]);
  return res;
}