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>

int n;
int A[20];

int adding(int m, int i){
	if( i >= n ){ return 0; }
	if( m < 0 ){ return 0; }
	if( m == A[i] ){
		return 1;
	}
	if( adding(m-A[i], i+1) ){ return 1; }
	if( adding(m, i+1) ){ return 1; }
	return 0;
}

int main(){
	int q, m;
	int i;
	char *ans[2] = {"no", "yes"};
	scanf("%d", &n);
	for( i = 0; i < n; i++ ){ scanf("%d", &A[i]); }
	scanf("%d", &q);
	for( i = 0; i < q; i++ ){
		scanf("%d", &m);
		printf("%s\n", ans[adding(m,0)]);
	}
	return 0;
}