Problem:
Score : 400 points

Problem Statement

Find the largest integer that can be formed with exactly N matchsticks, under the following conditions:

Every digit in the integer must be one of the digits A_1, A_2, ..., A_M (1 \leq A_i \leq 9).

The number of matchsticks used to form digits 1, 2, 3, 4, 5, 6, 7, 8, 9 should be 2, 5, 5, 4, 5, 6, 3, 7, 6, respectively.

Constraints

All values in input are integers.

2 \leq N \leq 10^4

1 \leq M \leq 9

1 \leq A_i \leq 9

A_i are all different.

There exists an integer that can be formed by exactly N matchsticks under the conditions.

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 ... A_M

Output

Print the largest integer that can be formed with exactly N matchsticks under the conditions in the problem statement.

Sample Input 1

20 4
3 7 8 4

Sample Output 1

777773

The integer 777773 can be formed with 3 + 3 + 3 + 3 + 3 + 5 = 20 matchsticks, and this is the largest integer that can be formed by 20 matchsticks under the conditions.

Sample Input 2

101 9
9 8 7 6 5 4 3 2 1

Sample Output 2

71111111111111111111111111111111111111111111111111

The output may not fit into a 64-bit integer type.

Sample Input 3

15 3
5 4 6

Sample Output 3

654

Solution in Rust (1.15.1) (judge verdict: Time Limit Exceeded)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*);
    }
}

#[allow(unused_imports)]
use std::cmp::{min, max};

#[allow(unused_imports)]
use std::io::Write;

fn main() {
    input!{
      n: i64,
      m: usize,
      aa: [i64; m],
    }
    // 1,2,3,4,5,6,7,8,9
    // 2,5,5,4,5,6,3,7,6
    let mut useable = [false; 10];
    for a in aa {
        useable[a as usize] = true;
    }
    if useable[7] {
        useable[6] = false;
        useable[9] = false;
    }
    if useable[9] {
        useable[6] = false;
    }

    if useable[1] {
        useable[4] = false;
    }

    if useable[5] {
        useable[3] = false;
        useable[2] = false;
    }

    if useable[3] {
        useable[2] = false;
    }

    // 2, 3, 5, 7
    let mut ans = vec![0; 10];
    let mut ans_size = 0;

    for d in (0..n/7+1).rev() {
        for b in (0..(n-d*7)/3+1).rev() {
            for c in 0..(n-d*7-b*3)/5+1 {
                let mut a = n - d*7 - b*3 - c*5;
                let mut b = b;
                let mut c = c;
                let mut d = d;
                if a < 0 || a%2!=0 {
                    continue;
                }
                a /= 2;

                if useable[4] {
                    if a % 2 != 0 {
                        continue;
                    }
                    a = a/2;
                }

                if useable[9] || useable[6]  {
                    if b % 2 != 0 {
                        continue;
                    }
                    b = b/2;
                }

                if ans_size > a+b+c+d {
                    continue;
                }

                let mut tmp = vec![0; 10];
                for num in (1..10) {
                    if !useable[num] {
                        continue;
                    }
                    if num == 8 {
                        tmp[num] = d;
                    }
                    if num == 9 || num == 6 || num == 7 {
                        tmp[num] = b;
                    }
                    if num == 2 || num == 3 || num == 5 {
                        tmp[num] = c;
                    }
                    if num == 1 || num == 4 {
                        tmp[num] = a;
                    }
                }
                if tmp.iter().sum::<i64>() != a+b+c+d {
                    continue;
                }

                if ans_size < a+b+c+d {
                    ans_size = a+b+c+d;
                    ans = tmp;
                    continue;
                }
                if ans_size == a+b+c+d {
                    let mut ok = false;
                    for num in (1..10).rev() {
                        if tmp[num] == ans[num] {
                            continue;
                        }
                        if tmp[num] > ans[num] {
                            ok = true;
                        }
                        break;
                    }
                    if ok {
                        ans = tmp;
                    }
                }
            }
        }
    }

    for num in (1..10).rev() {
        if !useable[num] {
            continue;
        }
        for i in 0..ans[num] {
            print!("{}", num);
        }
    }
    println!();
}