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)

fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let n: usize = iter.next().unwrap().parse().unwrap();
    let m: usize = iter.next().unwrap().parse().unwrap();
    let a: Vec<usize> = (&mut iter).take(m).map(|x| x.parse().unwrap()).collect();

    let mch = [0,2,5,5,4,5,6,3,7,6];
    let mut dp = vec![None;n+1];
    dp[0] = Some("".to_owned());
    for i in 0..n+1 {
        for &k in &a {
            if i + mch[k] >= n+1 {continue;}
            match (dp[i].clone(), dp[i+mch[k]].clone()) {
                (Some(p), Some(q)) => {
                    dp[i+mch[k]] = Some(cmp_max(&format!("{}{}", p, k), &q));
                },
                (Some(p), None) => {
                    dp[i+mch[k]] = Some(format!("{}{}", p, k));
                },
                _ => ()
            }
        }
    }
    println!("{}", dp[n].clone().unwrap());
}

fn cmp_max(a: &String, b: &String) -> String {
    if a.len() == b.len() {
        std::cmp::max(a.clone(), b.clone())
    } else if a.len() < b.len() {
        b.clone()
    } else {
        a.clone()
    }
}