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

bar = [0, 2, 5, 5, 4, 5, 6, 3, 7, 6]
bar2num = Hash.new(0)
A.each do |n|
  b = bar[n]
  bar2num[b] = n if n > bar2num[b]
end 

minbar = bar2num.keys.min
sz, r = N.divmod(minbar)
ansb = Array.new(sz, minbar)

for i in 0...[20, ansb.size].min
  bar2num.sort_by{|ar| -ar[1]}.each do |bar, num|
    if num > bar2num[ansb[i]] && r >= bar - ansb[i]
      r -= (bar - ansb[i])
      ansb[i] = bar
      break
    end
  end 
end 

t = [0, ansb.size - 20].max
(ansb.size - 1).downto(t).each do |i|
  bar2num.sort_by{|ar| -ar[0]}.each do |bar, num|
    if bar > ansb[i] && r >= bar - ansb[i]
      r -= (bar - ansb[i])
      ansb[i] = bar 
      break
    end 
  end
end
puts ansb.map{|b| bar2num[b]}.join