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: Accepted)

necessity = [2, 5, 5, 4, 5, 6, 3, 7, 6]
n, m = gets.split.map(&:to_i)
nums = gets.split.map(&:to_i)
nums.delete(4) if nums.include?(1)
nums.delete(2) if nums.include?(3) || nums.include?(5)
nums.delete(3) if nums.include?(5)
nums.delete(6) if nums.include?(7) || nums.include?(9)
nums.delete(9) if nums.include?(7)
nums.delete(5) if nums.include?(1) && nums.include?(7)
nums.delete(8) if nums.include?(1) && nums.include?(5)
num_sticks = nums.map { |n| [n, necessity[n - 1]] }
num_sticks.sort! { |a, b| (a[1] <=> b[1]).nonzero? || b[0] <=> a[0] }
selected_nums = Hash.new(0)
reduced_sticks = [(n - 30), 0].max
first_num, first_stick = num_sticks.first
div, mod = reduced_sticks.divmod(first_stick)
selected_nums[first_num] += div
rest_sticks = n - (reduced_sticks - mod)
queue = [[rest_sticks, selected_nums]]
options = []
until queue.empty?
  rest, selected = queue.shift
  if rest == 0
    options << selected
  else
    num_sticks.each do |num, stick|
      rest_dup = rest
      selected_dup = selected.dup
      if rest_dup >= stick
        rest_dup -= stick
        selected_dup[num] += 1
        queue << [rest_dup, selected_dup]
      end
    end
  end
end

ans = []
if options.size > 30
  options = options[-30..-1]
end
options.each do |hash|
  tmp = []
  hash.each do |k, v|
    v.times { tmp << k }
  end
  ans << tmp.sort { |a, b| b <=> a }.join.to_i
end
puts ans.max