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

cost = [0, 2, 5, 5, 4, 5, 6, 3, 7, 6]

dp = Array.new(N + 1) { Array.new(N + 1, '') }
dp[0][0] = '0'

ans = 0
i = 0

loop do
  updated = false

  N.times do |j|
    next if dp[i][j] == ''

    A.each do |n|
      total = j + cost[n]
      next if total > N

      dp[i+1][total] = [dp[i+1][total], dp[i][j] + n.to_s].max

      if total == N && ans < dp[i+1][total].to_i
        ans = dp[i+1][total].to_i
      end

      updated = true
    end
  end

  break unless updated
  i += 1
end

puts ans