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)

require 'pp'

R = [nil,2,5,5,4,5,6,3,7,6]

N,M = readline.chomp.split.map(&:to_i)
A = readline.chomp.split.map(&:to_i).sort.reverse

REQ = A.map {|a| R[a] }.uniq.sort
NUM = REQ.map {|r| A.find_all {|a| R[a]==r}.max }
# pp REQ,NUM

$max = 0
$max_matches = []
n_match = Array.new(REQ.size, 0)

def match_to_int(match)
  a = []
  match.size.times do |i|
    a += [NUM[i]] * match[i]
  end
  a.sort.reverse.map(&:to_s).join.to_i
end

def dfs(depth, n_match, n)
  #pp "#{depth}, #{n_match.inspect}, #{n}" if depth == n_match.size
  if depth == n_match.size
    if n == 0
      sum = n_match.inject(:+)
      if sum > $max
        $max = sum
        $max_matches = [n_match.dup]
      elsif sum == $max
        $max_matches << n_match.dup
      end
    end
    return true
  end

  r = REQ[depth]
  cur_digits = n_match[0..(depth-1)].inject(:+)
  return false if $max > cur_digits + n/r
  (0..n/r).to_a.reverse.each do |i|
    n_match[depth] = i
    b = dfs(depth+1, n_match, n-i*r)
    break unless b
  end
end

dfs(0, n_match, N)

puts $max_matches.map {|match| match_to_int(match) }.max