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: Accepted)

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

def match_matching(n, nums)
  dp = Array.new(n, nil)
  dp[0] = 0
  1.upto(n) do |i|
    nums.each do |num|
      j = i - MAP[num]
      next if j < 0 || dp[j].nil?
      dp[i] = [dp[i].to_i, dp[j] + 1].max
    end
  end

  remain_length = dp[n]
  ans = 0
  match = n
  while match > 0
    nums.reverse_each do |num|
      if match - MAP[num] >= 0 && dp[match - MAP[num]] == remain_length - 1
        ans = ans * 10 + num
        match -= MAP[num]
        remain_length -= 1
        break
      end
    end
  end
  ans
end

n, m = gets.split.map(&:to_i)
nums = gets.split.map(&:to_i)

puts match_matching(n, nums.sort)