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)
uses = [nil,2,5,5,4,5,6,3,7,6]

memo = [{}] # memo[桁][使用本数] = 値
as.each do |a|
  memo[0][uses[a]] = a
end

result = -1
1.upto(10e4) do |digit|
  memo[digit] = {}
  memo[digit-1].each do |cost, value|
    next if value.nil?
    next if cost > n
    if cost == n
      result = [result, value].max
      next
    end
    as.each do |a|
      next_value = (a * 10 ** (digit)) + value
      next_cost = uses[a] + cost
      if memo[digit][next_cost].nil? || next_value > memo[digit][next_cost]
        memo[digit][next_cost] = next_value
      end
    end
  end
  break if memo[digit].size == 0
end
puts result