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 Rust (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::cmp::{min, max};

struct Scanner<R: Read> {
    reader: R,
    buffer: String,
}

#[allow(dead_code)]
impl<R: Read> Scanner<R> {
    fn new(reader: R) -> Scanner<R> {
        Scanner { reader: reader, buffer: String::new() }
    }

    // fn line(&mut self) -> String {
    //     self.buffer = self.reader.by_ref().bytes().map(|c| c.unwrap() as char)
    //         .skip_while(|&c| c == '\n' || c == '\r')
    //         .take_while(|&c| !(c == '\n' || c == '\r'))
    //         .collect::<String>();
    //     self.buffer.clone()
    // }

    fn read_buffer(&mut self) {
        self.buffer = self.reader.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
    }

    fn safe_read<T: FromStr>(&mut self) -> Option<T> {
        self.read_buffer();
        if self.buffer.is_empty() {
            None
        } else {
            self.buffer.parse::<T>().ok()
        }
    }

    fn read<T: FromStr>(&mut self) -> T {
        if let Some(s) = self.safe_read() {
            s
        } else {
            // writeln!(std::io::stderr(), "Terminated with EOF").unwrap();
            std::process::exit(0);
        }
    }

    fn vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
        (0..len).map(|_| self.read()).collect()
    }

    fn mat<T: FromStr>(&mut self, row: usize, col: usize) -> Vec<Vec<T>> {
        (0..row).map(|_| self.vec(col)).collect()
    }
}

trait Joinable {
    fn join(self, sep: &str) -> String;
}

impl<U: ToString, T: Iterator<Item=U>> Joinable for T {
    fn join(self, sep: &str) -> String {
        self.map(|x| x.to_string()).collect::<Vec<_>>().join(sep)
    }
}

fn main() {
    std::thread::Builder::new()
        .stack_size(104_857_600)
        .spawn(solve)
        .unwrap()
        .join()
        .unwrap();
}

fn solve() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);

    let n = sc.read();
    let a: Vec<u32> = sc.vec(n);
    let mut flg = vec![false; 2001];
    for mask in 0..(1<<n) {
        let sum = (0..n).fold(0, |s, i| {
            if mask >> i & 1 == 1 {
                s + a[i]
            } else {
                s
            }
        }) as usize;
        if sum <= 2000 {
            flg[sum] = true;
        }
    }

    let q = sc.read();
    for _ in 0..q {
        let m: usize = sc.read();
        if flg[m] {
            println!("yes");
        } else {
            println!("no");
        }
    }
}