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)

pub 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> = iter.take(m).map(|x| x.parse().unwrap()).collect();

    // 添え字=数, 値=マッチの数
    let match_nums: [usize;10] = [0,2,5,5,4,5,6,3,7,6];

    // dp[i] := ちょうどi本で作れる整数の最大
    // dp[i+k] = dp[i] + 10 * max_digit_from_match(k)

    let mut dp = vec!["none".to_string();n+1];
    dp[0] = "".to_string();
    for i in 0..n+1 {
        for j in 0..m {
            let num_char = a[j];
            let match_num = match_nums[num_char];
            if i+match_num <= n && dp[i] != "none" {
                dp[i+match_num] = sdigit_max(
                    (&dp[i+match_num]).to_string(),
                    format!("{}{}", num_char.to_string(), (&dp[i]).to_string())
                );
            }
        }
    }

    println!("{}", dp[n]);
}

fn sdigit_max(a: String, b: String) -> String {
    if a == "none" {
        b
    } else if b == "none" {
        a
    } else if a.len() == b.len() {
        std::cmp::max(a, b)
    } else {
        if a.len() > b.len() {a} else {b}
    }
}