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)

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

def match_matching(n, nums)
  cost_to_num = {}
  nums.each { |n| cost_to_num[MAP[n]] = n }
  costs = cost_to_num.keys.sort

  counter = Hash.new { |h, k| h[k] = 0 }
  f = -> (i, rem) {
    if i == costs.size
      return rem.zero?
    end

    d = rem / costs[i]
    r = rem % costs[i]
    d.downto(0) do |j|
      counter[costs[i]] = j
      ret = f.call(i + 1, r + costs[i] * (d - j))
      return ret if ret
    end
    false
  }
  f.call(0, n)

  ret = ''
  cost_to_num.values.sort.reverse_each do |n|
    ret += n.to_s * counter[MAP[n]]
  end
  ret
end

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

puts match_matching(n, nums.sort)