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 (2.7.1) (judge verdict: Wrong Answer)

#!/usr/bin/env ruby

require 'set'

class Hash
  def push(key, value)
    self[key] = [] if self[key] == nil
    self[key].push(value)
  end
end

class Array
  def lower_bound(value)
    left = -1;
    right = self.length;
    while left + 1 < right
      mid = left + (right - left) / 2;
      if self[mid] >= value
        right = mid
      else
        left = mid
      end
    end
    right
  end

  def unique
    res = [self.first]
    each_cons(2) do |a, b|
      if a != b
        res.push(b)
      end
    end
    res
  end
end

def get_ints
  gets.chomp.split.map(&:to_i)
end

def get_ints_minus_one
  get_ints.map { |x| x - 1 }
end

def get_int
  gets.chomp.to_i
end


N, M = get_ints
A = get_ints
X = [0, 2, 5, 5, 4, 5, 6, 3, 7, 6]

if A.length == 1
  puts A[0].to_s * (N / X[A[0]])
else
  A.sort! { |a, b| (X[a] <=> X[b]).then { |x| x == 0 ? a <=> b : x } }
  ax = A.each_cons(2).map { |x, y| X[x] == X[y] ? nil : x }.compact
  ax.push(A.last) if X[A.last] != X[ax.last]

  min = ax[0]

  res = []
  test = ax[1..].map { |a| [a, X[a]] }
  test.unshift nil

  test.repeated_combination(7).each do |array|
    sum = array.map { |x| x ? x[1] : 0 }.sum
    div = (N - sum) / X[min]
    ama = (N - sum ) % X[min]
    if sum < N && ama == 0
      if array.compact.length == 0
        res.push min.to_s * div
      else
        xyz = array.compact.sort { |a, b| a[0] <=> b[0] }.reverse

        if xyz.first[0] > min
          res.push(xyz.map{ |x| x[0] }.join + (min.to_s * div))
        else
          res.push((min.to_s * div) + xyz.map { |x| x[0] }.join)
        end
      end
    end
  end

  puts res.sort { |a, b| (a.length <=> b.length).then { |x| x == 0 ? a <=> b : x } }.last
end