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)

N, M = gets.split.map(&:to_i)
as = gets.split.map(&:to_i)

a_to_count = [2, 5, 5, 4, 5, 6, 3, 7, 6].map.with_index do |n, i|
  [i + 1, n]
end.to_h

match_counts = as.map { |a| a_to_count[a] }.uniq
match_count_a = match_counts.map do |c|
  max_a = as.select { |a| a_to_count[a] == c }.max
  [c, max_a]
end.sort_by { |c, a| -a }

dp = Array.new(N + 1, nil)
dp[0] = [0, Array.new(9, 0)]
(0..N).each do |i|
  count, list = dp[i]
  next unless list
  match_count_a.each do |(c, a)|
    next if i + c > N
    t = list.dup
    t[9 - a] += 1
    if dp[i + c] == nil || ([count + 1, t] <=> dp[i + c]) > 0
      dp[i + c] = [count + 1, t]
    end
  end
end
ans = dp[N][1].each.with_index.reduce('') do |acc, (count, i)|
  a = 9 - i
  acc += a.to_s * count
end
puts ans