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.to_i
$lst = gets.split(' ').map(&:to_i).uniq.sort
lst = $lst

def rep(n)
  n_hash = {'1' => 2, '2' => 5, '3' => 5, '4' => 4, '5' => 5,
     '6' => 6, '7' => 3, '8' => 7, '9' => 6}
  n_hash[n.to_s]
end

def rep_r(n)
  return nil unless $lst.include?(n)
  n_hash = {'2' => [1], '3' => [7] ,'4' => [4] ,'5' => [2, 3, 5],
     '6' => [6, 9], '7' => [8]}
  n_hash[n.to_s]
end


min = lst[0]
lst.each_with_index do |n, i|
  if min < n && rep(min) >= rep(n)
    min = n
  end
end

if N % rep(min) == 0
  puts min.to_s * (N / rep(min))
else
  amari = N % rep(min)
  ret = min.to_s * (N / rep(min))

  i = -1
  loop do
    i += 1
    amari += rep(min)
    rn = rep_r(amari)
    if rn != nil
      if rn[-1] > min
        ret[i] = rn[-1].to_s
      else
        ret[-1-i] = rn[-1].to_s
      end
      break
    end

    amari2 = 0
    loop do 
      amari -= 1
      amari2 += 1
      rn2 = rep_r(amari2)
      if rn != nil
        if rn[-1] > min
          ret[i] = rn[-1].to_s
        else
          ret[-1-i] = rn[-1].to_s
        end
        break
      end
    end
  end
  puts ret
end