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 = gets.split[0].to_i

match_table = (1..9).to_a.zip([2,5,5,4,5,6,3,7,6]).to_h

digits = gets.split.map(&:to_i)

lookup_table = [2,5,5,4,5,6,3,7,6].zip((1..9).to_a).select do |a|
  digits.include?(a[1])
end.group_by {|a| a[0]}.map do |k, v|
  [k, v.map {|a| a[1]}.max]
end.to_h

how_matches = digits.map do |digit|
  match_table[digit]
end.sort

def test(n, nums)
  return if (!nums) or nums.empty?
  divisor = nums[0]
  q = n.div(divisor)
  r = n % divisor
  if r == 0
    Array.new(q, divisor)
  elsif nums.include?(r)
    Array.new(q, divisor) + [r]
  else
    list = nums[1..-1]
    (1..q).each do |i|
      res = test(n - divisor * (q - i), list)
      if res.kind_of?(Array) && !res.empty?
        return Array.new(q - i, divisor) + res
      end
    end
  end
end

ans = test(n, how_matches).map do |i|
  lookup_table[i]
end.sort.reverse.join('')

puts ans