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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n, m = gets.strip.split.map(&:to_i)
as = gets.strip.split.map(&:to_i)

@dict = {
    1 => 2,
    2 => 5,
    3 => 5,
    4 => 4,
    5 => 5,
    6 => 6,
    7 => 3,
    8 => 7,
    9 => 6,
}

@inv = {
    2 => 1,
    3 => 7,
    4 => 4,
    5 => 5,
    6 => 9,
    7 => 8,
}

availables = as.map { |a| @dict[a] }.sort

# 一番コスパのいい数字を並べまくる
min_cost = availables[0]

# 何桁並べられるか
num_digit = n / min_cost

# あと何本余っているか
residue = n % min_cost

# 本数を増やすことで大きい数字に変えられるか
def larger(num, as)
   # num を作るのに必要な本数
   match = @dict[num]
   # それより多い本数が必要な数字
   cand = @dict.select { |k,v| v > match && k > num && as.include?(k) }.keys
   return cand
end

# 本数を増やすことで小さい数字に変えられるか
def smaller(num, as)
    match = @dict[num]
    cand = @dict.select { |k,v| v > match && k < num && as.include?(k) }.keys
    return cand
end

d = @inv[min_cost]
digits = [d] * num_digit
while residue > 0 do
    # 最上位の数を大きい数字に変えられるか
    largers = larger(d, as)
    break if largers.empty?
    largers = largers.select { |l| @dict[l] <= residue }
    break if largers.empty?
    largest = largers.max
    digits.unshift(largest)
    digits.pop
    residue -= @dict[largest]
end

# 最下位の数を小さい数字に変えられるか
smallers = smaller(d, as)
largest = @dict.select { |k, v| v - @dict[d] == residue && smallers.include?(k)}.keys.max
digits.pop
digits.push(largest)

puts digits.join