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: Wrong Answer)

use std::collections::BTreeMap;

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

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n: usize = sc.read();
    let m: usize = sc.read();
    let a: Vec<usize> = sc.vec(m);
    let mut min_cost = 10;
    let mut max_num = 0;
    for &a in a.iter() {
        let cost = COSTS[a];
        if min_cost > cost || (min_cost == cost && max_num < a) {
            min_cost = cost;
            max_num = a;
        }
    }

    let mut map: BTreeMap<usize, usize> = BTreeMap::new();
    map.insert(0, 0);
    for _ in 0..10 {
        let mut next = map.clone();
        for (cur_cost, max) in map.into_iter() {
            for &a in a.iter() {
                let cost = COSTS[a] + cur_cost;
                let cur = next.entry(cost).or_insert(0);
                if *cur < max * 10 + a {
                    *cur = max * 10 + a;
                }
            }
        }
        map = next;
    }

    let s = n % min_cost;
    for i in 0.. {
        let m = i * min_cost + s;
        if let Some(&x) = map.get(&m) {
            let rest = (n - m) / min_cost;
            if x > max_num {
                print!("{}", x);
            }
            for _ in 0..rest {
                print!("{}", max_num);
            }
            if x <= max_num {
                print!("{}", x);
            }
            println!();
            return;
        }
    }
}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}