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

# p PRIORITY

@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
# p digits
# p "amari cost", @amari_cost
# p @res

cand_map = PRIORITY.select{|k, v| k <= @amari_cost}
p cand_map
if !cand_map.empty?
  to_add = cand_map.first
  @amari_cost -= to_add[0]
  if to_add[1][0] > @fst_digit
    @res = to_add.to_s + @res
  else
    @res += to_add.to_s
  end
end

# p PRIORITY
while @amari_cost > 0
  filtered = PRIORITY.select do |k, v| 
    ((k - @fst_cost) <= @amari_cost) && !v.select{ |value| value > @fst_digit }.empty?
  end

  if filtered.empty?
    break
  else
    @amari_cost -= filtered.first[0]
    @res.slice!(0, 1)
    @res.insert(0, filtered.first[1][0].to_s)
  end
end

puts @res