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)

#![allow(unused_mut)]
#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(unused_imports)]
#![allow(unused_macros)]
#![allow(dead_code)]
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($y: expr),+) => {
        cmp::max($x, max!($($y),+))
    };
}

macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($y: expr),+) => {
        cmp::min($x, min!($($y),+))
    };
}

const MOD: usize = 1_000_000_007;
const MAX: usize = 510_000;

struct BinCoeff {
    fac: Vec<usize>,
    finv: Vec<usize>,
    inv: Vec<usize>,
}

impl BinCoeff {
    fn new() -> BinCoeff {
        let fac = vec![0; MAX];
        let finv = vec![0; MAX];
        let inv = vec![0; MAX];
        let mut bincoeff = BinCoeff { fac: fac, finv: finv, inv: inv };
        bincoeff.com_init();
        bincoeff
    }

    fn com_init(&mut self) {
        let fac = &mut self.fac;
        let finv = &mut self.finv;
        let inv = &mut self.inv;
        fac[0] = 1;
        fac[1] = 1;
        finv[0] = 1;
        finv[1] = 1;
        inv[1] = 1;
        for i in 2..MAX {
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }

    fn bin_coeff(&mut self, n: usize, k: usize) -> usize {
        if k > n/2 {
            self.bin_coeff(n-k, k)
        } else {
            self.fac[n] * (self.finv[k] * self.finv[n - k] % MOD) % MOD
        }
    }
}

struct UnionFind {
    par: Vec<usize>
}

impl UnionFind {
    fn new(size: usize) -> UnionFind {
        UnionFind {
            par: (0..size).collect::<Vec<usize>>()
        }
    }

    fn root(&mut self, node: usize) -> usize {
        let parent = self.par[node];
        if parent == node { parent }
        else {
            let parent = self.root(parent);
            self.par[node] = parent;
            parent
        }
    }

    fn unite(&mut self, a: usize, b: usize) {
        let root_a = self.root(a);
        let root_b = self.root(b);
        self.par[root_b] = root_a;
    }

    fn is_same(&mut self, a: usize, b: usize) -> bool {
        let root_a = self.root(a);
        let root_b = self.root(b);
        root_a == root_b
    }
}

// must input n <= m
fn gcd(n: usize, m: usize) -> usize {
    if n == 0 {
        m
    } else {
        gcd(m%n, n)
    }
}

use std::{usize, iter, cmp};
use std::collections::{HashSet, BinaryHeap, VecDeque, HashMap};
fn main() {
    input! {
        N: usize,
        M: usize,
        A: [usize; M],
    }
    let cost = [std::usize::MAX, 2usize, 5, 5, 4, 5, 6, 3, 7, 6];
    let mut A: Vec<(usize, usize)> = A.into_iter().map(|a| (a, cost[a])).collect();
    A.sort_by(|&(a1, c1), &(a2, c2)|
        match c1.cmp(&c2) {
            cmp::Ordering::Equal => a2.cmp(&a1),
            ord => ord,
        });

    // 使わない数字を消す
    let mut ind = 1usize;
    while ind < A.len() {
        if A[ind-1].1 == A[ind].1 {
            A.remove(ind);
        } else {
            ind += 1;
        }
    }
    let mut numbers = [0; 9];
    let mut max_numbers = [0; 9];
    let mut max_len = 0usize;
    dfs(N, 1, &A, &mut numbers, &mut max_numbers, 0, &mut max_len);
    let ans: String =
        max_numbers.iter().enumerate()
            .flat_map(|(ind, &num)|
                iter::repeat(std::char::from_digit(9 - ind as u32, 10).unwrap()).take(num))
            .collect();
    println!("{}", ans);
}

fn dfs(rem: usize, ind: usize, A: &[(usize, usize)],
       numbers: &mut[usize], max_numbers: &mut[usize],
       n_len: usize, max_len: &mut usize) {
    if ind == A.len() {
        let (min_num, min_cost) = A[0];
        if rem % min_cost > 0 { return }
        let n = rem / min_cost;
        if n_len + n > *max_len {
            numbers[9 - min_num] = n;
            *max_len = n_len + n;
            max_numbers.clone_from_slice(numbers);
        } else if n_len + n == *max_len {
            numbers[9 - min_num] = n;
            if numbers > max_numbers {
                max_numbers.clone_from_slice(numbers);
            }
        }
    } else {
        let (num, cost) = A[ind];
        for n in 0..cost-1 {
            if rem >= cost * n {
                numbers[9 - num] = n;
                dfs(rem - cost*n, ind+1, A,
                    numbers, max_numbers,
                    n_len+n, max_len)
            }
        }
    }
}