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)
As = gets.split.map(&:to_i).sort

$h = Hash.new
HONs = [-1, 2, 5, 5, 4, 5, 6, 3, 7, 6]
As.each{|a| $h[HONs[a]] = a}
hons = $h.keys.sort

def p(str) end

def pack(n, hons)
  p "-----"
  p "n: #{n}"
  p "hons: #{hons}"
  ans = Hash.new(0)
  if hons.empty?
    return nil
  elsif n < hons[0]
    return nil
  elsif n % hons[0] == 0
    ans[hons[0]] = n / hons[0]
    return ans
  else
    min_i = n / hons[0] - 1
    #p "min_i: #{min_i}"
    new_hons = hons[1..-1]
    while min_i >= 0
      p "new_hons: #{new_hons}"
      p "remaining: #{n - hons[0]*min_i}"
      ans = pack_with_all_combi(n - hons[0]*min_i, new_hons)
      p "ans1: #{ans}"
      unless ans.nil?
        ans[hons[0]] = min_i
        p "ans2: #{ans}"
        return ans
      else
        min_i -= 1
        p "min_i2: #{min_i}"
      end
    end
    return nil
  end
end

def pack_with_all_combi(n, hons)
  #puts "#{[n, hons]}"
  ansA = []
  (1..hons.length).each do |i|
    hons.combination(i).each do |part_hons|
      ansA.push pack(n, part_hons)
    end
  end
  if ansA.all?{|ans| ans.nil?} then return nil end
  ansA.compact.max{|ans1, ans2| h2s(ans1).to_i <=> h2s(ans2).to_i}
end

def h2s(ans)
  ans.keys.map{|hon| [$h[hon], ans[hon]]}.
    sort{|ary1, ary2| ary2[0] <=> ary1[0]}.
    map{|a, n| a.to_s * n}.join('')
end

puts h2s(pack_with_all_combi(N, hons))