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)

def dfs(n,k,a)
  return nil if n<0
  if k==K.size
    return n.zero? ? a : nil
  end
  c=S[K[k]]
  r1=dfs(n-K[k], k, a+[c])
  r2=dfs(n, k+1, a)
  return r2 unless r1
  return r1 unless r2
  return r1 if r2.size < r1.size
  return r2 if r1.size < r2.size
  r1.sort.to_s < r2.sort.to_s ? r2 : r1
end

B=[0,2,5,5,4,5,6,3,7,6]

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

S=Hash.new{|h,k|h[k]=0}
A.each do |a|
  S[B[a]]=[S[B[a]],a].max
end
K=S.keys.sort

n,r=N.divmod(K[0])
until n.zero?
  n-=1
  r+=K[0]
  ok=dfs(r,0,[])
  next unless ok
  ok.sort!.reverse!
  i=0
  ok.each do |c|
    i+=1 if S[K[0]]<c
  end
  print ok[0...i]*""
  print S[K[0]].to_s*n
  print ok[i..-1]*""
  puts
  exit
end
raise if true