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: Wrong Answer)

#include <stdio.h>
#include <math.h>
#include <stdbool.h>

//????????????????????£?¨?.
void makeCombination(int *s, int n);
int sumup(int *s, int *a, int n);

int main(void) {
	int s[20] = { 0 };				//??????????????????.
	int a[20] = { 0 };				//???????????°.
	int n = 0;						//???????????°????????°.
	int sum = 0;					//????¨?.
	int q = 0;						//???????????°????????°.
	int m[200] = { 0 };				//?????´????????????????????°???.
	bool find = false;				//?????´????????????????????°.

	long long int i = 0;
	int j = 0;

	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[i]);

	for (j = 0; j < q; j++) {

		i = 0, find = false;			//?????????.

		while (i < (int)pow(2, (double)n) && find == false) {

			makeCombination(s, n);

			sum = sumup(s, a, n);

			if (sum == m[j]) {
				printf("yes\n");
				find = true;
			}

			i++;
		}

		if (!find)
			printf("no\n");
	}

	return 0;
}

//????????°??????????????????????????????.
void makeCombination(int *s, int n) {
	int i = 0;
	bool fin = false;

	while (!fin) {
		if (s[i]) s[i] = 0;
		else s[i] = 1, fin = true;
		i++;
	}
}

//????????°???????¶?????????????.
int sumup(int *s, int *a, int n) {
	int sum = 0;
	int i = 0;

	for (i = 0; i < n; i++)
		if (s[i]) sum += a[i];

	return sum;
}