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)

# require 'byebug'

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

match_numbers = [nil, 2, 5, 5, 4, 5, 6, 3, 7, 6].map.with_index {|e, i| [e, i]}.select {|e, i| as.include?(i) }.sort.to_h

# p match_numbers
# p match_numbers.to_h

dp = Hash.new(0)
(1..n).each do |i|
  tmp = match_numbers[i].to_i.to_s
  # p tmp
  # byebug
  match_numbers.keys.each do |k|
    unless dp[i-k].zero?
      a = dp[i-k].to_s
      b = match_numbers[k].to_s
      str = a < b ? (b+a) : (a+b)
      if tmp.length < str.length || (tmp.length==str.length && tmp < str )
        tmp = str
      end
    end
  end
  dp[i] = tmp.to_i
end

# p dp
p dp[n]