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)

N_MATCH, NUMBERS = gets.split(' ').map(&:to_i)
USABLE = gets.split(' ').map(&:to_i).sort.reverse
TABLE = [1000,2,5,5,4,5,6,3,7,6]

PRIORITY = USABLE.reduce({}){ |z, x| (z[TABLE[x]] ||= []) << x; z }.sort.to_h

@fst_cost = PRIORITY.first[0]
@fst_digit = PRIORITY.first[1][0]
digits = N_MATCH / @fst_cost
amari_cost = N_MATCH % @fst_cost
@res = @fst_digit.to_s * digits

if amari_cost == 0
  puts @res
  exit(0)
end

def dfs(amari, nums = [])
  return nil if (amari < 0)
  return nums if (amari == 0)
  res = nil
  PRIORITY.each do |num, v|
    res ||= dfs(amari - num, nums.clone << v[0])
  end
  res
end

amariyou = nil
denomi = 0
while !(amariyou = dfs(amari_cost))
  amari_cost += @fst_cost
  denomi += 1
end
@res.slice!(0, denomi)

lg = amariyou.select { |v| v > @fst_digit }.sort.reverse.map(&:to_s).join
sm = amariyou.select { |v| v < @fst_digit }.sort.reverse.map(&:to_s).join

puts lg + @res + sm