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: Accepted)

use std::io::{stdin, Read};

macro_rules! parse {
    ($it: ident ) => {};
    ($it: ident, ) => {};
    ($it: ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
    ($it: ident, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
}

macro_rules! parse_val {
    ($it: ident, [$t:tt; $len:expr]) => {
        (0..$len).map(|_| parse_val!($it, $t)).collect::<Vec<_>>();
    };
    ($it: ident, ($($t: ty),*)) => {
        ($(parse_val!($it, $t)),*)
    };
    ($it: ident, $t: ty) => {
        $it.next().unwrap().parse::<$t>().unwrap()
    };
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    parse!(it, n: usize, m: usize, mut a: [usize; m]);
    let b = [0, 2, 5, 5, 4, 5, 6, 3, 7, 6];
    a.sort();
    a.reverse();
    let mut dp = vec![None; n + 1];
    dp[0] = Some(0);
    let mut prev = vec![0; n + 1];
    for i in 0..(n + 1) {
        if let Some(dpi) = dp[i] {
            for &ai in a.iter() {
                let j = b[ai];
                if i + j > n {
                    continue;
                }
                dp[i + j] = match dp[i + j] {
                    Some(dpij) if (dpi + 1 <= dpij) => dp[i + j],
                    _ => {
                        prev[i + j] = i;
                        Some(dpi + 1)
                    }
                };
            }
        }
    }
    let mut ret = vec![];
    let mut cur = n;
    loop {
        for &ai in &a {
            if cur < b[ai] {
                continue;
            }
            if let Some(dpnext) = dp[cur - b[ai]] {
                if cur >= b[ai] && dpnext == dp[cur].unwrap() - 1 {
                    ret.push(ai);
                    cur = cur - b[ai];
                    break;
                }
            }
        }
        if cur == 0 {
            break;
        }
    }
    println!(
        "{}",
        ret.iter()
            .map(|&i| i.to_string())
            .collect::<Vec<_>>()
            .join("")
    );
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}