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: Time Limit Exceeded)

N, M = gets.split.map(&:to_i)
COSTS = [0,2,5,5,4,5,6,3,7,6]
# A = gets.split.map(&:to_i).sort_by {|a| COSTS[a]}
A = gets.split.map(&:to_i).sort.reverse

MIN = A.map do |a|
  COSTS[a]
end.min

def solve(num, match)
  if match <= 0
    return num
  end

  max = 0
  max_digit = (match - COSTS[A.first]) / COSTS[A.first]
  # p "max_digit: #{max_digit}"

  used = {}
  A.each do |a|
    c = match - COSTS[a]
    if c >= 0 && used[c].nil? && c / MIN >= max_digit
      # p "choose: #{a}"
      used[c] = true
      n = solve(num * 10 + a, c)
      if max < n
        max = n
      end
    end
  end

  return max
end

p solve(0, N)