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::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

const COST: [usize; 10] = [0, 2, 5, 5, 4, 5, 6, 3, 7, 6];

fn calc(n: usize, usable: &Vec<usize>, memo: &mut Vec<String>) -> String {
    if n == 0 {
        return "".to_string();
    }
    if memo[n] != "" {
        return memo[n].clone();
    }
    let mut ret = "NG".to_string();
    for &v in usable.iter() {
        if COST[v] > n {
            continue;
        }
        let nn = n - COST[v];
        let nret = calc(nn, usable, memo);
        if nret == "NG" {
            continue;
        }
        let nret = format!("{}{}", v, nret);
        if ret == "NG" || nret.len() > ret.len() || (nret.len() == ret.len() && nret > ret) {
            ret = nret;
        }
    }
    memo[n] = ret.clone();
    return ret;
}

fn main() {
    let n = read::<usize>();
    let m = read::<usize>();
    let mut usable = vec![0; m];
    for i in 0..m {
        usable[i] = read::<usize>();
    }
    let mut memo = vec!["".to_string(); n + 1];
    for i in 1..n {
        calc(i, &usable, &mut memo);
    }
    let ans = calc(n, &usable, &mut memo);
    println!("{}", ans);
}