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.split.map(&:to_i)
as = gets.chomp.split

h = Hash.new("0")

table = {
  "1" => "2",
  "2" => "5",
  "3" => "5",
  "4" => "4",
  "5" => "5",
  "6" => "6",
  "7" => "3",
  "8" => "7",
  "9" => "6"
}

as.each do |a|
  h[table[a]] = [a, h[table[a]]].max
end

keys = h.keys
dp = Hash.new("0")
(1..n).each do |i|
  tmp = h[i.to_s]
  keys.each do |k|
    k = k.to_i
    if dp[i - k] != "0"
      a = dp[i - k].to_s
      b = h[k.to_s].to_s
      str = a < b ? (b + a) : (a + b)
      if tmp.length < str.length || tmp < str
        tmp = str
      end
    end
  end
  dp[i] = tmp
end

puts dp[n]