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>
#define TRUE 1
#define FAULSE 0
#define N 20
#define M 2000

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

int main (){
    int q, A[N], Q[M], i;

    //input area
    scanf("%d", &n);
    for (i = 0; i<n; i++)
	scanf("%d", &A[i]);
    scanf("%d", &q);
    for (i = 0; i<q; i++)
	scanf("%d", &Q[i]);

    //check whether we can synthesize the A-number frome the Q-number
    for (i = 0; i<q; i++){
	if (solve(A, 0, Q[i]) == TRUE )
	    printf("yes\n");
	else 
	    printf("no\n");
    }
    return 0;
}

int solve(int A[], int x, int m ){

    if (m == 0)
	return TRUE;
    
    if (x >= n)
	return FAULSE;

    if (solve( A, x+1, m-A[x] ) == TRUE) return TRUE; //choice version
    if (solve( A, x+1, m) == TRUE) return TRUE;//non-choice version
    else 
	return FAULSE;
}